Fulham are heading back to the Championship after just one year in the top flight.
Their relegation was confirmed last night after defeat to Watford and fans are fearing the worst over their playing squad – expecting it to be picked apart.
But Davies, the club’s record goalscorer after two spells stretching 11 years, says he’s heard two key players want to stay put.
“I was talking to somebody on Saturday and I know it’s hearsay but he is a family friend of the Cairneys,” he said on Love Sport radio.
“As far as he was aware, [Cairney’s] father says that he is going nowhere and he’s is staying next year.
“The other rumour I heard was that Mitrovic is staying. That would be great from a supporter’s point of view.
“I’d love to be able to say that Sessegnon is going to stay but with only a year left on his contract, the likelihood is that he will be sold.
“But I’m hoping that he is sensible enough, even if it is Tottenham or Liverpool, to put in his contract that he should be loaned back to Fulham for a season.
“He’ll then play another 46, 50 games for us [which is important] from an experience point of view.
“If he did go to a Premier League game, he may only play four or five cup games and be stuck in U23 or reserve football.
“At the moment, I’m happy that we’re going to keep two of them and fingers crossed we get a loan for Sess to come back and we keep all three.
“Then we will be in with a chance of coming back up.”
Fulham were blown away by Watford in the second half after holding them to a 1-1 draw at half time, and were eventually beaten 4-1.
It ends the possibility of another season in the top flight after going through three managers this year.
Scott Parker is in charge until the end of the season but could be replaced again in the summer.
“I’m gutted,” he said after last night.
“I realised how big the task was, we all understood how big the task of staying in the division was, but the most disappointing thing is the way we lost today.
“That’s just us in a snapshot. If you haven’t watched us this season but then saw that period when two, three and four went in, that’s us.
“I’m sure there’s a mental issue. When you’re at the bottom, everything becomes a lot harder. There’s been a naivety in certain instances of certain games, and that was prevalent tonight.
“The dressing room is obviously disappointed. Everyone is gutted, as you can imagine. It’s a squad of players who have been relegated, so they’re disappointed.”