The Red Devils have already had a £40million bid for the defender rejected by Crystal Palace, but are ready to go back in with a higher offer.
Wan-Bissaka enjoyed a sensational season with the Eagles last campaign, and Solskjaer is keen to get the transfer over the line to prevent against a bidding war.
But are United right to splash such cash on a right-back when they have other areas to strengthen and, perhaps more interestingly, have Diogo Dalot?
Portuguese right-back Dalot was signed by Jose Mourinho for £19million as a work in progress back in 2018.
After his first match in a Red Devils shirt, Mourinho said of him: “I want to be also nice to Luke [Shaw] because I think both play at the same level. I think Diogo and Shaw, they played very, very, well.
“Our danger came from both, both of them. They had fantastic movement, they had depth, they had crosses, they had assists.
“They were involved in the most dangerous actions and they defended also well. So I think both of them, they were very, very good.
“But of course Luke is here for a few years, he’s playing since the beginning of the season and for Diogo first match for the club after a knee surgery.
“I think very good, solid performance. I think everyone could see the potential and everyone could see that he’s a 19-year-old player who has more than 10 years to play for Manchester United.”
Dalot showed real signs of improvement last season, but Solskjaer believes the defender is a little too raw to be considered United’s first choice right-back.
What’s more, Solskjaer has shown on occasion that he sees him as more of a right midfield player instead of an out and out defender.