Liberal Democrat MP David Laws is said to be unwilling to return to government after the stress of being outed as gay over his expenses claims.
Mr Laws was Chief Secretary to the Treasury for less than three weeks in May. He stood down after it was revealed he had paid £40,000 of taxpayers' money in rent to his partner James Lundie.
Until then, he had kept his sexuality a secret.
Prime minister David Cameron and deputy Nick Clegg are understood to be keen to see him return to the cabinet if he is cleared by a parliamentary investigation.
The MP did not attend his party's conference this week and a source told the Sun: "Everybody is saying when will David be allowed to come back, but the truth is he doesn't want to be a minister again. He's lost the hunger."
According to the Daily Mail, Mr Laws has told friends that he may step down as MP for Yeovil at the next election, depending on the findings of the report.
The newspaper added that he is working on a book titled 22 Days in May, which will be an account of how the coalition came to power and his own personal trauma.