Mr Vaz, 59, a married father of two, quit as chairman of the influential House of Commons Home Affairs committee on Tuesday after becoming embroiled in a scandal over male prostitutes.
The Leicester East MP also had a conversation regarding cocaine with one of two male escorts, in which the MP said he did not want to use the drug, but indicated that he would pay for it for the other man at a later date, according to the Sunday Mirror.
In the wake of the revelations, Conservative MP Andrew Bridgen indicated that he would be writing to Scotland Yard calling for Mr Vaz to be investigated for misconduct in a public office and conspiracy to supply controlled substances.
Scotland Yard released a statement yesterday saying: “Following allegations in the Sunday Mirror on Sunday 4 September concerning a Member of Parliament, the Metropolitan Police Service can confirm a letter was received on Wednesday, 7 September requesting police consider the matter. The letter has been forwarded to the Met’s Special Inquiry Team, part of Specialist Crime and Operations, to assess and identify what criminal offences – if any – may have been committed.
“At this stage a police investigation has not been launched.”
Announcing his resignation on Tuesday, Mr Vaz said: “Those who hold others to account must themselves be accountable.”
He had come under increasing pressure following claims that he paid two male escorts he met at a flat he owns near his family home in north London last month.
He said: “It is in the best interest of the Home Affairs Select Committee that its important work can be conducted without any distractions whatsoever. I am genuinely sorry that recent events make it impossible for this to happen if I remain chair.
“I have always been passionate about select committees, having served as either chair or member for half of my time in Parliament. The integrity of the select committee system matters to me.”
He insisted he was “immeasurably proud” of the work the committee has carried out over the last nine years.
Mr Vaz said the decision to resign and stand aside immediately was “my decision, and mine alone”.
He had faced claims that the committee’s investigations into issues including prostitution could be undermined if he remained as chairman.