Giggs a front-runner to replace Caldwell
Bookmakers Skybet had the Manchester United as 7/4 favourite for the hot-seat at first, though he later slipped to 9/4 behind Karl Robinson (5/4).
Giggs has been out of football since leaving his post at Old Trafford in the summer.
Dougie Freedman and Steve Evans were both at 10/1, with Nigel Pearson and Tim Sherwood at 12/1.
Current assistant Graham Barrow (14/1) is fancied ahead of sacked England boss Sam Allardyce (16/1).
Incredibly, Malky Mackay was listed on the Skybet long-list at 20/1 - despite being sacked by chairman David Sharpe.
And former Latics managers Paul Jewell (20/1), Roberto Martinez and Uwe Rosler (both 33/1) are linked with the post, as well as former midfield favourite Jimmy Bullard (50/1).
Sharpe says he wants a manager who will make an immediate impact to propel them away from the bottom-three, suggesting he will act swiftly.