"The club offered David a three-year extension to his contract on fantastic money before I took charge, but it appears he has options elsewhere," Davies told the club's official website.
"There is only so much you can do to try and persuade a player to stay at the club.
"Our first priority was to get David Healy to stay at Preston North End, but he feels that he wants to wait and see what is happening and that is disappointing.
"I am still hopeful and not totally resigned to losing David just yet."