Married father-of-two paid for the men to visit him one evening last month at a flat he owns in London, it claims.
The Leicester East MP, who is chairman of the Home Affairs Select Committee which monitors crime and drugs policy, said he was referring the claims to his solicitor and would be seeking advice.
Several newspapers say Mr Vaz, 59, is stepping down as committee chairman.
However, Mr Vaz did not comment on those reports in a statement to the BBC.
He said: “It is deeply disturbing that a national newspaper should have paid individuals to have acted in this way.
“I have referred these allegations to my solicitor Mark Stephens of Howard Kennedy who will consider them carefully and advise me accordingly.”
A Labour Party spokesman said: “Keith Vaz has issued a statement on this matter. As with all departmental select committees, Keith was elected to the chair of the Home Affairs Select Committee by the House of Commons, and his position is a matter for him and the House.”