The Metropolitan Police have said they will look into allegations against Keith Vaz, and "assess and identify what criminal offences - if any - may have been committed".
The Labour MP also had a conversation about cocaine with one male escort where he said he did not want to use the drug, but suggested he would pay for it for the other man at a later date, according to the Sunday Mirror.
In the wake of the revelations, Tory MP Andrew Bridgen indicated that he would be asking Scotland Yard to investigate for misconduct in a public office and conspiracy to supply controlled substances.
Scotland Yard released a statement on Friday saying: "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."
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Two women have been arrested for trying to travel to Syria to join a proscribed organisation.
The pair, aged 16 and 20, were arrested in central London on Sunday evening on suspicion of preparation of terrorist acts.
Officers from the Met Police Counter Terrorism Command arrested a 20-year-old woman and a 16-year-old girl on suspicion of preparation of terrorist acts, namely travelling to Syria to join a proscribed organisation.
They were arrested in central London at approximately 9pm on Sunday, August 21. Both were taken into custody at a central London police station.
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Bottles and other objects thrown by revellers left some police officers injured.Read the full story ›
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A "shocking" under-representation of black and minority ethnic people within UK police forces requires "radical action," a committee warns.Read the full story ›
Pc Rytis Gilys was found guilty of sexual assault after twice touching a female colleague inappropriately on her leg inside a patrol car.Read the full story ›