The 18-year-old midfielder emerged as a surprise target for the Red Devils in the final hours of the summer window, only for the two clubs to fail to agree terms before it slammed shut on Tuesday night.
Page still turned out for Leicester the same evening, playing the full 90 minutes and setting up the opener in a 2-0 win over Plymouth Argyle in League One.
According to the Manchester Evening News, the clubs had actually moved closer to an agreement than first thought, but Leicester are holding out for a fee above the £12.5m package Manchester City paid for fellow academy graduate Jeremy Monga earlier in the summer.
Had a deal for Page gone through, he was expected to spend the season back on loan at Leicester rather than moving to Old Trafford immediately.
The report suggests the sticking point is not the overall valuation but the structure of the package, with the two clubs still at odds over add-ons and payment terms. Page himself is understood to favour the move.
It remains unclear whether Page, an England youth international who has represented his country at Under-17, Under-18 and Under-20 level, would go straight into United's first-team plans or join one of the club's development sides if a transfer is eventually completed. He is currently playing regular senior football for Leicester in League One, having established himself as a first-team regular there this season.
Manchester United's business in the market was relatively restrained by their recent standards. Having already brought in Carlos Baleba, Andrey Santos and Youri Tielemans earlier in the window, the club opted against further late additions despite an apparent need for more defensive cover, and also turned down a loan approach from Everton for Joshua Zirkzee.
Speaking before the window closed, head coach Michael Carrick said he was satisfied with the summer's business.
"We went into the window wanting to come out stronger from the group we had last season and we have definitely added to that," he said. "Certainly, the players we have brought into the group absolutely delighted with, think we have done some really good business."