The 20-year-old completed a £72million move to Old Trafford from Atalanta in the summer but has struggled in front of goal.
Hojlund has netted five times in the Champions League but has only scored one goal in the Premier League.
He did so at the 15th time of asking when he fired in United's late winner in a 3-2 victory at home against Aston Villa on Boxing Day.
Even though his efforts up front have had limited success, Hojlund's age suggests there is a lot more room for improvement.
And Casemiro feels there is still a lot more to come from the Dane and has tipped him for success at United.
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Speaking to the club website, Casemiro said: "At the end of the day, he's just a kid, so we shouldn't be putting a lot of pressure on him.
"A lot of people think that he should be coming in and scoring 30-odd goals right away. He's still young and this is his first season in the Premier League."
Casemiro was referred to a moment during United's defeat at Arsenal after Hojlund came off the bench and was a nuisance for defenders.
The former grabbed the latter's shirt and appeared to celebrate his efforts, and has now explained why he was so pleased with him.
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"Regarding the footage you mentioned, I was really happy with his attitude. The thing is, it's really difficult when you come on in such a demanding game, as games against Arsenal are.
"When he entered the fray he contributed a lot, changing our dynamic, so I tried to express to him just how I was feeling. He's definitely playing better in every game and he's working really hard. Rasmus is a dedicated lad and he's keen to kick on.
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"He'll be a great player for this club and, with the ambitions he has, he could define an era at Manchester United."