It follows several weeks of speculation that United is keen on Maguire, with a report earlier this week claiming that the ex-Hull defender is 'confident' the move will happen before the deadline.
The latest from Sky Sports is that United is actually beginning to formalize its interest and has now established contact with the Foxes.
The report claims that United is willing to pay £65m for Maguire, who will shortly return from a post-World Cup holiday, although it is also said that Leicester is determined not to sell.
Riyad Mahrez has already left the club in a £60m deal this summer, and while ex-United defender Jonny Evans has been brought in, Leicester do not wish to lose another big name.
Maguire himself appears ready to jump ship after admitting that, despite being happy at the King Power Stadium, he now has ambitions to play at a higher level after the buzz of the World Cup.
"Every player wants to play at the highest level," he said recently.
"I've just come back from playing at a World Cup, where I really enjoyed the high pressure of the games. It was something that I really thrived off."
"Leicester have been unbelievable to me and I'm really happy there but I'm also an ambitious player and everyone wants to play at the top."