Mr Cohen is stepping down at the election
Labour MP Harry Cohen is being investigated by the police over his expenses claims, the BBC understands.
Mr Cohen, who is standing down at the election, was stripped of a £65,000 pay-off for retiring MPs after a "serious" breach of expenses rules.
The BBC's Daniel Sandford said no file on the Leyton and Wanstead MP had been sent to the Crown Prosecution Service.
It comes as three Labour MPs and one Tory peer charged over their expenses claims are due to appear in court.
All four - Labour MPs Elliot Morley, Jim Devine, David Chaytor and Tory peer Lord Hanningfield - deny the allegations and say they will defend themselves "robustly".
The police have not confirmed Mr Cohen is being investigated as part of its almost 10-month inquiry into expenses claimed by Parliamentarians and it is not known what the inquiry relates to or what stage it is at.
They have said only that a "small number of cases remain subject to consideration by a joint Metropolitan Police and Crown Prosecution Service assessment panel or are subject to continuing investigation".
Mr Cohen apologised to Parliament last month after he was criticised for claiming more than £70,000 in second home allowances for a property in his constituency at a time his designated main home was being let out for long periods.
A report by the Parliamentary Standards Commissioner found that the second home "could not be regarded as his home for the purpose of claiming parliamentary allowances" as he was not living there.
As an MP from an outer London constituency, the report said he should instead have claimed a London supplement that would have entitled him to £9,000 over the same period.
Consequently, the report concluded that Mr Cohen received more than £60,000 in public money "to which he was not entitled".
The Standards and Privileges Committee, which has the power to recommend sanctions for MPs over their expenses, said the breach was particularly serious and involved a large sum of public money.
It said it had "sympathy" for the MP because his wife had been battling serious illness while the MP said his circumstances were unusual because his wife's illness required them to spend more time in the constituency.
Mr Cohen argued he had always designated it as his main home and there were periods when it was not let and he was living there.
Mr Morley, Mr Devine, Mr Chaytor and Lord Hanningfield will appear at City of Westminster Magistrates' Court on Thursday after being charged with false accounting last month in relations to their expenses claims.
The four face charges of false accounting under section 17 of the Theft Act 1968. If found guilty they face a maximum sentence of seven years' imprisonment.
At the time charges were brought, the three MPs said they "totally refute any charges that we have committed an offence".