According to The Mirror, the United legend will leave his current role at Old Trafford and an official announcement will be made in the next few days.
The Welshman has been the assistant manager at United since the days of David Moyes.
Giggs worked under Louis van Gaal for the past two seasons, but it has been reported by The Mirror that he will turn down the chance to work with new United manager Jose Mourinho.
According to latest odds on Skybet, Giggs is the favourite to take over at Forest.
The 13-time Premier League winner’s odds of becoming the new manager of the Championship club are 1/2.
Former West Ham United boss Gianfranco Zola is second favourite with odds of 9/4, while ex-Olympiacos and Marseille manager Michel’s odds are 6/1.
Forest fans have taken to Twitter to discuss the possibility of Giggs becoming the manager of the first team.
Below are some of the best comments:
Not Ryan Giggs pleaseee too risky especially for how long we have failed to do anything in the league dispite what manager we have #nffc— Dunni (@Forest_Lad_1994) June 19, 2016
If #nffc appoint Giggs, the Greek guy has lost the plot - please be rumour and nothing more— AJ (@Lad87Red) June 19, 2016
Giggs is not a manager or a coach. At best, he babysat Man Utd for a few matches and then became Van Gaals lacky #nffc— Lincoln Rob (@leahdan1) June 18, 2016
Pearson was odds on. Evans was odds on. Poyet was odds on. Zola was odds on. Why should the current odds mean that Giggs has the job? #NFFC— Woof Zip Criminal (@fritzromanov) June 18, 2016
#nffc need a manager with experience in the championship giggs is a huge risk plus fawaz usually sacks managers every few months— Fareed (@CMfkhalid9) June 18, 2016