Several bookmakers on Wednesday stopped taking bets on markets involving a possible exit for the former Valencia boss, who joined Liverpool in 2004.
Molby was aware rumours had been spreading regarding how long Benitez will remain in charge and told Sky Sports News: "I'd be surprised if Rafa were to walk out on Liverpool. We do know for a while he's been unhappy about certain things, but I still think it would take a big man to walk out on Liverpool at such a crucial stage of the season."
The former Denmark international added: "Whereas some people are quite happy to back Rafael Benitez to be gone by the end of the week, I would rather take the odds on him being Liverpool manager next Monday.
"I heard the rumours myself on Tuesday night, and they have been gathering pace, everyone's talking about it."
However Molby will not take the talk of Benitez's possible departure too seriously for now.
He said: "I think the people who say it can't happen might just prove to be spot-on."