Giggs was 28/1 to become Forest’s next manager at the start of the day, but he is now the 1/2 favourite with SkyBet.
Twitter rumours have suggested that Giggs has already been offered the Reds’ job, although these are totally unconfirmed reports.
Giggs’ is currently employed by Manchester United, but his future is uncertain.
The former Welsh international is known to have held hopes of managing at Old Trafford, but he was overlooked in favour of Jose Mourinho.
Giggs will not continue as assistant manager under Mourinho, but he has been told that he can have any other job that he wants with the Red Devils.
Despite this offer, Giggs is yet to commit his future to United, leaving some to suggest that he is about to leave Old Trafford for the first time during his professional career.
If Giggs did become Forest manager it would finally end a lengthy search for the Midlands club, who have been without a permanent boss for over three months now.