United will pay £80 million for the 26-year-old, with the deal subject to a medical and personal terms, though with Maguire keen to make the step up the latter should prove no obstacle, The Independent reported.
Solskjaer declined to comment on the Maguire deal during an interview ahead of the International Champions Cup game with Milan in Cardiff on Saturday.
But United boss Solskjaer told PA, “We still hope one or two deals can be done. We’ve been working on cases for a long time and suddenly the deal can be done when it’s dragging on.
“As a club we’ve had targets, but as a coach and manager when you go out on the pitch you have to work with the ones you have.
“You can’t think ‘what if he comes’ or ‘if he’s sold’.
“The reality is you have to work with the ones that are there. I’ve never been thinking ‘I’ll play him there but he’s coming in’.
“Everyone who has been in preseason has a big part to play and most of them have impressed.
“But it (transfer speculation) doesn’t stop (after the deadline) because you still have to plan for the next transfer window and next summer.”
The Maguire deal represents success for both parties, with United getting a ball-playing defender who offers the ideal mix of both experience and relative youth, while Leicester’s strategy of holding its ground over its valuation of the player has paid off.
The Foxes will receive a world-record fee for a defender, eclipsing the £75 million Liverpool paid Southampton for Virgil Van Dijk in January 2018.
United had made strengthening the center of its defense a priority at the start of the summer, with the need only becoming more acute when Eric Bailly suffered a knee injury during United’s preseason tour of China which is expected to keep him out for at least four months.
However, Maguire’s arrival will almost certainly lead to a clear-out at Old Trafford, where there are already six defenders – Bailly, Victor Lindelof, Phil Jones, Chris Smalling, Marcus Rojo and Axel Tuanzebe – in the senior squad.
The deal more than doubles United’s outlay this summer so far. Aaron Wan-Bissaka cost an initial £45 million from Crystal Palace while Daniel James signed from Swansea for £18 million.