Manchester United, Juventus, Real Madrid are all tracking the Swiss 20-year-old star.
The 20-year-old is currently on loan at Basel from Red Bull Salzburg, and has impressed this season, particularly in the Champions League where he's notched three goals in four games.
Italians champions Juventus are the latest side to join the fold after the youngster was being tracked by Real Madrid and Manchester United, however the Red Devils reportedly rejected him when he was 17 and that could play into the hands of their competitors for his signature.
He has indeed spoken of the possibility of an earlier move to Old Trafford, saying: "The transfer almost happened. In the end I decided otherwise. My parents had allowed me to transfer, but I did not. I would have started at the Under-18s, the way into the first team would have been far. The competition would have been massive."
Oberlin is a Swiss under-21 international, however he was born in Cameroon and is eligible to play for them as he is yet to feature in a senior international fixture. Manchester United fans will get a proper glimpse of him in a fortnight or so when Basel host United in the Champions League.