Stephen Crabb has apologised after admitting to sending "explicit" messages to a 19-year-old woman he interviewed for a job in 2013, according to the Mail.
The married MP was quoted by the paper as saying he had been "foolish" but that there had been no sexual contact.
"We exchanged messages which talked about sex but none of it was meant seriously," he was quoted as saying.
"We met for coffee a few times and had a glass of wine once at the Commons, but nothing more.
"I accept any kind of sexual chatter like this is totally wrong and I am sorry for my actions."
Mr Crabb resigned last year as Work and Pensions Secretary following reports of a similar incident.
The reports come amid speculation at Westminster that at least four MPs have been caught up in various allegations of sexual misconduct.
Downing Street said such behaviour was "completely unacceptable" and urged women affected to report it to the police.
Labour leader Jeremy Corbyn warned of a "warped and degrading culture" where the abuse of women had gone unchallenged for too long.
Environment Secretary Michael Gove was forced to apologise on Saturday after a "clumsy" attempt at a joke in which he likened being interviewed by BBC presenter John Humphrys to "going into Harvey Weinstein's bedroom".
ITV Wales has contacted Mr Crabb's office for a comment.