The combination of the biggest cellphone carrier in the United States and Apple's smash-hit phone would certainly be a powerful one. And it would be a major challenge to AT&T, which has been the exclusive carrier for the phone since its debut in 2007.
But Verizon could decide that it does not actually need the iPhone, thanks to its deepening ties with Google.
In big cities, AT&T's network has buckled under the data-heavy demands of the iPhone, frustrating customers. Verizon has managed to avoid similar problems while working with Google, Apple's latest nemesis, to offer several strong rivals to the iPhone that use the Android operating system from Google.
On Thursday, Verizon will begin selling the Droid X, an Android phone that many say may be the fiercest challenge yet to the iPhone, Steven P. Jobs's crowning creation.
"Verizon is back in the game, even without the iPhone," said Craig Moffett, an analyst at Sanford C. Bernstein & Company.
Despite the pull of the iPhone, Verizon has managed to steadily increase its share of the smartphone market, to 26 percent in May, from 20 percent in late 2008. In the same period, AT&T's market share slipped to 40 percent, from around 45 percent, according to comScore. Those numbers do not take into account the impact of the popular iPhone 4, released last month.
Before the original iPhone's debut, AT&T and Apple signed a five-year exclusive deal that is due to expire in 2012, according to court documents that emerged in a class-action lawsuit against Apple. Only insiders know whether that agreement has been amended.
When the phone proved to be a hit, Verizon appeared to be left out of the race for versatile phones running programs from third-party developers. Verizon was also not particularly friendly with Google, whose participation in an auction of precious wireless spectrum angered Verizon executives. Google wanted to force the federal government to require carriers to make their networks more open to a wide range of devices and software. Verizon executives were furious, vowing that they would not support the Android operating system.
A year later, Verizon recognized the threat posed by the iPhone and began working with Google and Motorola to develop the first of its Android phones, which it sold under the name Droid, a trademark it licensed from Lucasfilm.
Verizon has since collaborated closely with Google to develop six phones running Android, helping to give Google's mobile operating system 13 percent of the smartphone market in the United States. In contrast, Apple has a 24 percent share, while Research In Motion, maker of the BlackBerry, commands nearly 42 percent.
T-Mobile and Sprint have also jumped on the Android bandwagon. Matt Carter, president of Sprint's 4G division, said the company was building a portfolio of smartphones that could run on its fourth-generation wireless network, including the Evo, an Android phone made by HTC.
"Obviously, we would love to have the iPhone, but we feel the HTC Evo is a better phone," he said.
The success of its Android phones has emboldened Verizon to take shots at Mr. Jobs and the iPhone. A recent ad slyly referred to the controversy over the iPhone 4's antenna design in boasting that the Droid X "allows you to hold the phone any way you like and use it just about anywhere to make crystal-clear calls."
"Verizon is behaving as if it's not going to get the iPhone anytime soon," said Charles Wolf, an analyst at Needham & Company. "The signal I'm getting from the intimacy of Google and Verizon is that it is certainly an engagement, if not a marriage."
Reports from analysts and the news media have predicted, with almost comic regularity, an iPhone debut on Verizon in the next week, next month or next year. Representatives for Verizon and Apple declined to comment on the matter.
Neither company will rule out the possibility of an eventual union. For Apple, millions of untapped Verizon customers are at stake. Analysts say that a partnership between the two companies could double Apple's smartphone share -- a crucial jump if Mr. Jobs hopes to stay ahead of Google.
At a technology conference last month, when Mr. Jobs was asked whether the iPhone could appear on rival networks, he replied that "the future is long."
John Stratton, chief marketing officer at Verizon, said in an interview that his company "had a lot of respect" for Apple.
"They have served the industry very well," he said. "The smartphone category is now growing faster than any other part of our business, and in no small part, that is something we can trace back to the creation of the iPhone."
A Verizon-Apple coupling faces some obstacles. In particular, Verizon maintains an ironclad grip over the phones on its network, steering marketing campaigns, stamping each device with a prominent logo and often installing its own applications, like its VZ Navigator mapping program.
An Apple executive, speaking on the condition of anonymity because he was not authorized to discuss the matter publicly, said Apple would never agree to put another company's name on the iPhone.
Then there are business factors. After Mr. Jobs visited rival carriers, AT&T secured the iPhone in part because it offered the most favorable terms. Analysts estimate that Apple brings in an average of more than $650 for each iPhone sold. Consumers pay upward of $200, and AT&T subsidizes the rest.
Verizon, on the other hand, pays far less than $300 for Android, BlackBerry and Palm phones, said Shaw Wu, an analyst at Kaufman Brothers.
Verizon has "done well with the network rollout, they have done well with the financial side of the equation, and they have maintained control by owning the Droid brand," Mr. Wu said. "Verizon has proven that they don't necessarily need Apple."
In addition, Verizon and Google may have agreed to share the revenue generated by sales of Android applications, something Apple does not do, said Philip Cusick, an analyst at Macquarie Research Equities. "Verizon would be uncomfortable ceding those things to Apple," he said.
Perhaps, he said, it won't need to. "If Verizon didn't get the iPhone, it wouldn't be the end of the world," he said. "They would continue to add subscribers and new phones."
But there are also signs that Verizon is willing to compromise to get what remains the world's most coveted phone. Mr. Stratton of Verizon said the company was relaxing its control over the phones on its network and was even willing to sacrifice that logo.
"We don't have a hard and fast set of rules we think we need to operate under anymore," Mr. Stratton said.
One person who seems to believe a Verizon iPhone is a certainty -- and is comfortable with that eventuality -- is Eric E. Schmidt, chief executive of Google. In an interview last month, he said a Verizon iPhone would not bother him.
"I think they should do what they need to do to make their data network and revenue stronger," he said. "I am satisfied that the Droid would do well against an iPhone on the same data network."