An announcement is likely to be made in the next 24 hours to officially confirm Maguire as a United player.
And asked for an update on Maguire’s arrival after the clash with Milan, Solskjaer told reporters: "Hopefully the last little details will be in place and hopefully we can announce something soon.”
Maguire has featured regularly for Leicester throughout pre-season but missed their clash with Atalanta at the King Power Stadium on Friday as an agreement for a move to United was reached.
And with the centre-back fully fit, the Norwegian hinted he could name Maguire among his starting line-up for their opening Premier League clash against Chelsea a week tomorrow.
What Ole Gunnar Solskjaer said when asked about Harry Maguire to Man Utd announcement (Image: GETTY)
What Ole Gunnar Solskjaer said when asked about Harry Maguire to Man Utd announcement (Image: GETTY)
What Ole Gunnar Solskjaer said when asked about Harry Maguire to Man Utd announcement (Image: GETTY)
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Hopefully the last little details will be in place and hopefully we can announce something soon
Ole Gunnar Solskjaer
The manager added: “Let's get the last details over the line but yeah, he's played a few games over the summer so we'll have to assess him if and when."
Speaking on Friday night, Leicester boss Brendan Rodgers also suggested the deal was on the verge of completion.
“As it stands of course there’s been contact between the two clubs. A fee has been agreed.
“Then it’s a case of him having the opportunity to speak to them and see if they can come to an agreement over personal terms.
“That’s something that’s of interest to him – and then of course a medical.
What Ole Gunnar Solskjaer said when asked about Harry Maguire to Man Utd announcement (Image: GETTY)
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“After that there is not a great deal more to say. Probably after the weekend – one way or another we will know more.
“But clearly the two clubs have been talking and have agreed a fee.”
Maguire will become United's third signing of the summer after Daniel James and Aaron Wan-Bissaka, taking their total summer spending to around £140m.
The 26-year-old's fee will make him the most expensive defender of all time, surpassing the £75m Liverpool paid for Virgil van Dijk over 18 months ago.
The move will also see Maguire become United's second-most expensive signing ever, after £89m midfielder Paul Pogba.