The Red Devils boss is eager for Old Trafford chiefs to be quick out of the blocks in the summer transfer window.
Solskjaer is looking for reinforcements all over the park, with a host of big names on the club’s radar.
A string of talent including Kalidou Koulibaly, Jadon Sancho, Nicolas Pepe and Moussa Dembele have been linked.
But Manchester United’s first signing this summer appears likely to be a lesser-known player.
According to the Evening Standard, Solskjaer is hopeful a deal for Swansea winger Daniel James will be agreed imminently.
The fee for the Wales international will reportedly rise to £20m with add-ons.
Solskjaer believes James is capable of solving the team’s problem position on the right wing.
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The United boss is a big fan of the 21-year-old’s lightning speed.
A swoop for James has been prioritised after ruling out Bournemouth star Ryan Fraser.
The 25-year-old was being monitored by United but the club fear his price would be inflated thanks to his fine season.
Despite having one year left on his Cherries contract, Fraser is likely to cost more than James.
The transfer window is open until the eve of the next Premier League season but Solskjaer wants all their business done before the start of July.
When asked about James last week, United boss Solskjaer said that he hopes the club will get their transfer business done quickly.
“I don’t know how many names have been mentioned, there are players I have barely seen who it says we are going to sign!” he said.
“The earlier you can do the transfers, the better it is.
“I can’t comment on every single individual.
“I don’t like when others talk about my players, I won’t talk about others.”