Elanga will have a medical in Nottingham over the weekend before becoming the second signing of the summer for Steve Cooper.
The Sweden international has rejected offers from Everton, West Ham and Marseille to join Forest, who agreed a fee with United earlier on Friday. Elanga will end a nine-year association with United to move to the City Ground.
Forest are also close to capturing Ola Aina, the Nigeria international, as Cooper ramps up his preparations for the forthcoming season.
Aina will to join Forest on a free transfer after flying into Spain on Friday to undergo a medical at the club’s training base in Valencia. The 26-year-old is available after leaving Serie A club Torino at the end of last season.
A former Chelsea trainee, Aina can play as a right-back or wing-back and his most recent Premier League experience was a loan spell at Fulham in the 2020/21 season.
Forest are working on a number of other signings with a new goalkeeper the No 1 priority.
Manchester United’s Dean Henderson remains their top target and talks are understood to have progressed in the last 24 hours. Henderson impressed on loan at the City Ground last season and is currently recovering from a thigh injury.
Forest are also seeking another goalkeeper, a left-back and a central midfielder as they prepare for their second successive season in the top division.
Cooper’s planning in Spain have sustained some disruption after centre-back Moussa Niakhate dislocated his elbow in the friendly against Valencia. Niakhate is expected to miss at least six weeks with the injury.
Meanwhile, Forest defender Harry Toffolo has agreed an extension with the Football Association for his response to 375 alleged breaches of gambling laws.
Toffolo is facing a potentially lengthy ban from football following the charge and his request for more time to prepare his reply has been accepted by the FA, with the date moved from this Wednesday to July 26.
The 27-year-old could face heavy sanctions after the FA’s investigation into activity over a three-year period running from 2014 to 2017.
Ivan Toney, the Brentford forward, was banned from football for eight months in May after he admitted 232 breaches of the FA’s Rule E1 (b) which prevents any footballer from making any type of bet on the game.