According to UK media reports, the names include several senior Tories who are accused of hounding, propositioning or groping young women in Parliament or their constituencies.
"Any reports of sexual harassment are deeply concerning," a Downing Street spokesperson said.
"Any allegations that may come to light will be taken extremely seriously and we would advise people to contact the police if there is such an allegation so that it's fully investigated," she said.
The Prime Minister is reportedly given a regular briefing by the Tory chief whip, Gavin Williamson, on misdemeanours by party MPs after morning planning meetings at her 10, Downing Street office.
One of May's aides told 'The Sunday Times' that the briefing was known in Downing Street as "the ins and outs" chat.
Insiders say it covers MPs having affairs, suffering from sex addiction, caught using prostitutes, running up gambling debts and taking illegal drugs.
"Gavin would come in and explain that this MP was having an affair or that MP had been up to no good. The 'ins and outs' stuff, the whips call it. Theresa just sits there and doesn't say much. On one occasion she said, 'Why can't they just do their job?,'" an aide was quoted as saying.
Metropolitan Police have reportedly dealt with nine cases of sexual harassment in Parliament this year.
But following the Hollywood scandal involving disgraced mogul Harvey Weinstein and the 'Me Too' campaign on social media with women speaking out against their tormentors, House of Commons Speaker John Bercow is to hold a meeting next week to discuss greater safeguards for researchers and parliamentary staff.
"The Prime Minister was very clear when we responded to the reports about Harvey Weinstein in the last few weeks that any unwanted sexual behaviour is completely unacceptable, and that is true in any walk of life - including politics," the Downing Street spokesperson said.
UK Education Secretary Justine Greening said anyone who felt they had been sexually harassed should contact the police.
Opposition Labour party leader Jeremy Corbyn has also said that MPs who abuse or sexually harass women must be "held to account".
According to 'The Sun', those accused in a so-called "sleaze dossier" include a married Tory minister alleged to have made passes at several women, including journalists and aides.
One Tory MP is dubbed the "Lift Lunger" after groping a woman who found herself alone in a lift with him.
Another is known as "Happy Hands" for constantly touching women under the table at meetings.
A third is nicknamed "Taxi Tickler" after repeatedly grabbing at young women in the back of shared cabs, with new recruits allegedly warned, "He is not safe in taxis".
Meanwhile, it also emerged that a secret group of the BBC's top female presenters, including Pakistani-origin presenter Mishal Husain, has uncovered a string of suspected cases of sexual harassment at the corporation, including by a senior sports presenter.
The group, which keeps its membership of senior editors and presenters a closely guarded secret, has been encouraging and then supporting colleagues to report claims to BBC management.