David Laws, the former cabinet minister, may face a police fraud investigation into his expenses claims.

The Liberal Democrat MP had to resign as Chief Secretary to the Treasury in May after it emerged he claimed £40,000 in second home allowance to rent rooms from his long-term partner James Lundie.

Commons rules ban MPs from renting accommodation from their partners and Mr Laws said he had only claimed the money to keep his homosexuality secret.

According to the Sunday Times, informed Commons sources said police will focus on his claims for utility, telephone and other household bills and will “almost certainly” progress to a formal investigation.

Mr Laws consistently claimed round figures for maintenance, telephone and utilities bills. Before changes to claim limits came in during March 2008, he regularly claimed £150 a month for utilities and £200 a month for service and maintenance.

Speaking to the Chard and Ilminster News today in his constituency, he said: “We have had no approach whatsoever from the police. This may therefore be mischief making by other political parties.

“There is a review going on by the Parliamentary Standards Commissioner, which I asked him to undertake following the events of the past few weeks.”

Prime minister David Cameron and his Liberal Democrat deputy Nick Clegg are understood to be keen to see Mr Laws make a comeback to the cabinet as soon as possible, but a police investigation would make this difficult.

In June, Mr Laws said his friends and family had accepted his sexual orientation “without hesitation” and that he had been “pretty stupid” to keep it secret.