Luke Shaw however is in contention to make his return from injury at Goodison Park.
Hojlund, 20, limped off in United’s 1-0 win over Luton Town ahead of the international break, appearing to suffer a hamstring injury.
His countryman Christian Eriksen was also an injury casualty that afternoon, forced off in the first-half after suffering a knee injury. Both players were forced to withdraw from the Denmark squad as a result.
A club statement last week confirmed Eriksen is facing a month on the sidelines with Hojlund’s injury not as bad as first feared.
Speaking on Thursday, ten Hag played down the striker’s chances of featuring at Goodison Park on Sunday but suggested he will be given every opportunity to prove his fitness before then.
‘Christian will take a little bit longer,’ Erik ten Hag told the Premier League. ‘It will take some weeks until he will return.
‘Rasmus Hojlund, not too bad. Everton will be a close finish but we’re working on that.
‘We’re not sure if he can make that but, hopefully, in the next week, he will return to the squad.’
United have two pivotal fixtures next week away from home, first heading to Galatasaray in a game they must win to keep their hopes of qualifying for the knockout stages of the Champions League alive.
They then head to St James’ Park next Sunday to take on Newcastle United, who thrashed United at Old Trafford to dump them out of the Carabao Cup in early November.
Shaw meanwhile could make his return to the side this weekend. The left-back has not played since suffering a muscle injury in September but was back in training this week ahead of the trip to Merseyside.
‘Luke Shaw has been training for two weeks with the team,’ ten Hag said. ‘We are quite hopeful that he will return to the squad for Sunday’s game.’
Andre Onana, who picked up a shoulder injury on international duty with Cameroon, has also trained this week.
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