The young centre-back enjoyed a successful spell on loan over the past 18 months with Aston Villa, who want to bring him back in a permanent deal.
However, the 21-year-old wants to try and break into the first-team at United.
The Sunsays manager Solskjaer will sit down with the Englishman at Carrington before the club flies out for their preseason tour on July 8.
An Old Trafford source - via The Sun - said: "Axel had a few injury issues at Villa but there is no doubt he is a top prospect.
"The manager will be happy to sit down and let him know where he stands at some point in the near future.
"The fact is the club are heading in a new direction with a greater emphasis on young players, so Axel could be in with a good shot."