The two clubs are locked in a battle over the England international, who will be allowed to Leicester City this summer for the right price.
United are confident they have the power to outbid the Premier League champions but know they will be forced to pay an even higher premium because City are prepared to make Maguire the most expensive player in their history.
Like United, the Premier League champions have not been put off by Leicester’s valuation of around £90million for the centre back.
Neither club is willing to go that high but City’s determination to see Maguire fill the void created by Vincent Kompany’s departure means United will have to get significantly closer to Leicester’s asking price.
Swansea winger Daniel James is their only signing so far, while Wan-Bissaka’s move is expected to be completed imminently.
But in a summer when Solskjaer hopes to sign as many as five new players, the United manager wants his squad in place for the start of pre-season training on July 1.
It’s claimed Maguire’s preference is City and the chance to win major honours under Guardiola. But he sparked fresh speculation about his future over the weekend when ‘liking’ a tweet linking him with United.
He later explained it was an accident, but he was convinced he’d join United when they first expressed interest 12 months ago – and Solskjaer will have to hope Old Trafford remains a draw.
City are also ready to consider alternatives if his price gets too high, but it’s understood Koulibaly is not under consideration, despite claims they’ve already tabled an offer for the Napoli defender.