The 2-0 defeat to Stuttgart at Ibrox on Tuesday night left them bottom of the table with two points from five games and without even the consolation of a Europa League spot.
The loss of income from no European competition could see the board selling off their more saleable assets in the transfer window.
Asked if he feared players leaving in January, Davis said: "I hope not.
"That will probably be out of the manager's hands but hopefully we can keep this group together.
"I'm sure the manager would like to bring in a couple of players to freshen things up as well.
"But that will be down to the people who run the club."