The Cabinet Office is to investigate whether International Trade Minister Mark Garnier broke the Ministerial Code after he admitted asking his secretary to buy sex toys.
The married International Trade Minister described the incidents as "good-humoured high jinks" and "amusing conversation," according to the Mail on Sunday.
He was said to have strongly denied that they constituted sexual harassment.
The report comes after Downing Street warned on Friday that Theresa May would take "serious action" against any minister found to have acted inappropriately.
Meanwhile, former Conservative cabinet minister Stephen Crabb was reported to have admitted sending "explicit" messages to a 19-year-old woman after a job interview at Westminster.
Neither Mr Garnier nor Mr Crabb could be contacted for comment.
Mr Garnier's former secretary Caroline Edmondson told The Mail on Sunday he had given her the money to buy two vibrators at a Soho sex shop - one for his wife and one for a woman in his constituency office.
Ms Edmondson, who has since left to work for another MP, was quoted as saying that on another occasion in a bar, in front of witnesses, he told her: "You are going nowhere, sugar tits."
The Mail reported that Mr Garnier had admitted the claims, saying: "I'm not going to deny it, because I'm not going to be dishonest. I'm going to have to take it on the chin."
According to the paper, he said the "sugar tits" comment was part of an "amusing conversation" about the TV comedy Gavin and Stacey, while the sex toys were bought after a Christmas lunch.
"We bought some soap sets, that sort of stuff, scented candles. The vibrator shop was high jinks," he is quoted as saying.
"I hung around outside and she went into this shop. That was it."
The Mail said Mr Garnier had conceded that, in the current climate, his actions could look like "dinosaur behaviour", but insisted: "It absolutely does not constitute harassment."
In the case of Mr Crabb, the Mail said that he had sent "explicit" messages to a 19-year-old woman he interviewed for a job in 2013, when he was a Welsh minister.
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 a cabinet minister 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".
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