The Labour MP from Leicester since 1987, who is a married father of two,paid for men to visit him one evening last month at a flat he owns in London, the 'Sunday Mirror' claimed.
The 59-year-old Goan-origin MP has since announced he will be stepping aside as chair of the influential House of Commons Home Affairs Committee, which he has headed for the past 10 years.
It is understood that Vaz has not resigned completely but temporarily as he speaks to his lawyer and other members of the committee.
The committee is currently examiningprostitution in the UK and had issued a report recently saying thatsoliciting by sex workers should be decriminalised.
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It isalleged the MP had two meetings with Eastern European-origin escorts, including a 90-minute meetingon August 27.
One text, reportedly sent by Vaz, said the men should arrive at "11 pm, nice and late".
He is said to have added: "I want a good time please."
Vaz is accused of asking the young men to bring poppers to the flat, as well as allegedly joking about being a "pimp".
He also spoke about having had unprotected sex.
And ahead of the meeting, he had allegedly sent a series of texts in which he jokingly called himself one of the men's "pimp" and "bank manager".
Vaz paid the escorts in cash, the report claimed.
"Money was also paid into a bank account used by one of them by a man linked to a charity set up by the MP," it said.
A Labour Party spokesperson said: "Keith Vaz has issued a statement on this matter.