O’Riley moved from MK Dons to Celtic for £1.5m in January and has already caught the eye of United, who are understood to be monitoring his development in the Scottish Premiership – as per the Manchester Evening News.
The midfielder managed three goals and two assists in 12 outings during the second half of last season for Celtic and has since hit the ground running in 2022/23.
In five league outings, he has provided three assists for the Hoops, two of which came on Sunday as Celtic put nine past Dundee United.
O’Riley was born in London but has since switched international allegiance to Denmark. He made his under-21 debut for the Danes back in March of 2022.
However, Manchester United fans should not expect the 21-year-old to be arriving anytime soon as sources say there is no suggestion of an imminent approach for O’Riley.
O’Riley is under contract with the Scottish powerhouse until 2026. No potential transfer fee is mentioned in the report from the MEN.
The player himself, meanwhile, recently stated he has no plans to leave Celtic.
Speaking to bold.dk, the Danish U21 international said: “Yes, there are some clubs who have inquired about me. I can’t say which clubs, though. But while it’s great to know there’s a lot of interest in me, I’ve only got one thing on my mind and that’s to do well for Celtic.
“I have no plans to leave Celtic, so if nothing happens, nothing happens, and that’s fine. I’m really happy to be at the club where we’re also going to play the Champions League, which I’m really looking forward to. It’s huge.
“I am aware and have heard about the interest from some of the big clubs, but I must admit that it is not something that I think about so much.”