According to The Athletic, the move is subject to the player passing a medical with Forest, with the newly promoted side set to cover his full salary for the duration of his stay.
Steve Cooper's side are keen to strengthen their squad this summer after securing their long-awaited return to the Premier League via the play-offs.
With current number one Brice Samba facing an uncertain future following a contract stalemate, the Reds are keen to bring in a goalkeeper with experience in the top flight.
Henderson certainly fits the bill on that front.
After being a part of the Sheffield United side that secured promotion in 2018/19, Henderson was brought back to Bramall Lane the following year as Chris Wilder's Blades secured a rather impressive ninth place finish in the top flight.
Since then, Henderson has been back with his parent club at Old Trafford and challenging David de Gea for a spot in the starting XI. However, the 25-year-old has been limited to just 29 appearances for the Red Devils.
The hope for the goalkeeper will be that regular first-team football at the City Ground will aid his hopes of securing a spot in England's squad for the 2022 World Cup in Qatar later this year.
Speculation over Henderson's future has been rumbling on for some time, with former United goalkeeper Mark Bosnich telling talkSPORT in October that he should leave the club 'as soon as he possibly can' and that he needs to 'look after himself'.
"I think he should go," Bosnich told talkSPORT Breakfast. "He's at the stage of his career where he needs to be playing regular football.
"He'll know that as well. I understand that at the start of the season, him having a go in pre-season to see how things plan out.
"De Gea has been excellent and there's no doubt about it, but I think from Dean Henderson's point of view, he needs to start looking after Dean Henderson.
"He should go and should go as soon as he possibly can."