The 19-year-old midfielder has established himself as a influential first-team member with Swedish outfit Mjallby since making his senior debut in November 2021.
Rosengren made 29 appearances across all competitions in his breakthrough season with the Swedish top-flight club, providing three assists, and has since started five of his six outings at the beginning of the 2023 campaign.
Mjallby's sporting director Hans Larsson has revealed that Man United are "looking" at the highly-rated teenager, who has also attracted interest from clubs in the Netherlands and Denmark.
Larsson has also refused rule out the prospect of selling Rosengren - who is under contract with the Swedish club until December 2025 - in the near future.
Speaking to Danish news outlet Tipsbladet, Larsson said: "There have been some Danish, English and a Dutch club looking at him. Viborg FF, [Aarhaus] and Manchester United, among others, have been looking at him.
"There is nothing concrete about him. There have been some rumours, and then several clubs have looked at him."
Asked if Mjallby are prepared to sell Rosengren this summer, Larsson added: "We must wait and see. It's his first year as a real first-team player in Allsvenskan, and I'm not so sure he wants to leave either. We'll have to wait and see what happens."
Larsson acknowledged in a separate interview with Fotbollskanalaen that Man United have sent scouts to watch the Sweden Under-21 international on "several" occasions.
"I think it's been several times actually, at least based on what they told me, but I haven't met anyone," said Larsson. "They have only contacted and said that they will come, because they want tickets.
"I don't want to put too much pressure on Otto, but there have also been a couple of Danish and Dutch clubs who have been here.
"It's really nice (for Man United to visit), absolutely. It's a sign that Mjallby are working properly, and he's their own product, so it's wonderful."
Rosengren is not the only teenage starlet to have been linked with Man United, as Erik ten Hag's side are reportedly considering a swoop for Ajax wonderkid Amourricho van Axel Dongen.