Alex boss Davis took the reins at Gresty Road in November 2011, replacing Gradi after he opted to move upstairs having first been appointed as manager back in 1983.
In his 18 months at the helm, Davis has led to Crewe to promotion via the League Two play-off final, returned to Wembley to lift the Johnstone's Paint Trophy and kept the club in League One with a commendable 13th-placed finish.
His stock has risen so much that Birmingham-born Davis - a boyhood Wolves fan - has now become odds-on favourite to take over at Molineux.
Gradi has told Crewe's official website: "Steve has done a great job and he and Neil (Baker, assistant) work well together. They are a good combination and have worked hard to bring success to the club.
"I am not surprised that his name crops up when jobs are mentioned because his record is very good. He has won a promotion, won a cup and finished halfway in the league above.
"If you would have asked them to have done that for us when he first took over, he would probably and understandably turned around and said that it couldn't possibly be done, but he has gone and done it.
"Steve is unflappable and knows how the club works. He knows he has to make the money we lose by promoting young players and selling them on. You can only do that by developing young players and putting them in."
Davis has overtaken ex-Millwall boss Kenny Jackett and former England manager Steve McClaren as frontrunner for the Wanderers hot seat.