Roma face Ukraine's Shakhtar Donetsk at home in the first leg of their Champions League last 16 tie on Wednesday having not won in three Serie A games.
Fans protested at training following Saturday's 2-0 home defeat by Napoli which left last term's runners-up in eighth spot.
An American consortium Di Benedetto was given a 30-day exclusive negotiation period on Tuesday to discuss a purchase of the cash-strapped club with media reports saying Ranieri's job could be at risk.
"Three or four months ago I talked with the lads and I asked 'is there a problem with me? If so I'll leave.' They said no and here we are," Ranieri told a news conference.
"I did it because for us it's a very particular season. It's useless to deny it. The situation with the club's future that we are going through is obviously an influence."
"A coach is like a husband. He is the last to know about certain things. Don't ask me if Montella is coming but I think it's just Roman gossip," he said.
Defender Philippe Mexes, sat alongside his coach, confirmed that Ranieri had asked for and got the squad's backing.
"We are giving our utmost but it's the players who are guilty primarily," the Frenchman added.
