The Denmark international has missed his new side's opening two matches of the campaign against Wolverhampton Wanderers and Tottenham Hotspur due to a back issue.
However, Hojlund has been training in the early weeks of the season, and according to The Sun, Red Devils head coach Erik ten Hag hopes to be able to select him in the squad for Saturday's game with Forest.
The report claims that a start is out of the question due to his lack of action, but there is a chance that the 20-year-old could be named among the substitutes with a view to featuring at some stage of the match.
Hojlund completed a move to the 20-time English champions on August 5, signing a five-year contract with the club after an agreement was reached with Atalanta BC for his transfer.
The Dane scored 10 goals and registered four assists in 34 appearances for Atalanta during the 2022-23 campaign following his arrival from Sturm Graz.
Hojlund is one of three new signings at the club this summer, with Mason Mount and Andre Onana also arriving to boost the squad.
Onana will again be between the sticks on Saturday, but Mount is facing a spell on the sidelines with an injury that he picked up against Tottenham last weekend.
Man United are believed to be keen to make two more signings before the transfer window closes, with a new midfielder and goalkeeper on the agenda.
Fiorentina's Sofyan Amrabat is thought to be the club's leading midfield target, although it remains to be seen whether a deal for the Moroccan can be done before the deadline.
Amrabat is currently training alone at Fiorentina and has not been included in their squad for Thursday's Europa Conference League playoff first leg with Rapid Vienna due to the speculation surrounding his future.
There will have to be outgoings, though, with Harry Maguire, Eric Bailly, Donny van de Beek and Scott McTominay among those being linked with departures.
In terms of the goalkeeping spot, Dean Henderson is allegedly in discussions over a switch to Crystal Palace, which could lead to Fenerbahce's Altay Bayindir being introduced to provide competition for Onana.
Man United beat Wolves 1-0 in their Premier League opener at Old Trafford on August 14, but they will enter the clash with Forest off the back of a 2-0 defeat at Tottenham in North London.