Ms Irani, who is Minister for Textiles and Information and Broadcasting, is also a Rajya Sabha MP from Gujarat.
Gujarat's top post was seen as reserved for outgoing chief minister Vijay Rupani before assembly election results were announced on Monday. The BJP could not win even 100 seats, stalling at 99, 16 short of their tally in the last election, in the face of a spirited fight by the Congress.
The lower margin of victory is said to have changed Mr Rupani's status as sure-to-be-next-CM. He remains a frontrunner, but in Delhi today top BJP sources told NDTV that the party will "discuss before going ahead." Earlier this year, BJP chief Amit Shah had announced that Mr Rupani would be chief minister again. But now, the sources said, the party will have to recalibrate its strategy ahead of the 2019 national election, when Prime Minister Narendra Modi will seek a second term.
In 2014, when the BJP stormed to power led by Mr Modi, then chief minister of Gujarat, the state had given all 26 parliament seats to the party. The assembly election result this year has signaled that the BJP will have to work hard to repeat that performance.
Mr Rupani is seen as close to Amit Shah and has a clean image, but the Congress' attack on the BJP on issues of local development have reportedly brought his candidacy into question.
In this year's Gujarat election, the Congress played on the anger of these key groups against the ruling BJP, posting its best result in decades. The opposition party has won 80 seats, 19 more than last time.
Patel leaders, outgoing deputy chief minister Nitin Patel and state BJP chief Jeetu Vaghani, as well as union minister Purshottam Rupala are in the race for Chief Minister, as is current minister of state for home Pradeepsinh Jadeja.
Union Finance Minister Arun Jaitley will go to Gujarat later this week to oversee the selection of the next chief minister.