But it has been claimed Brendan Rodgers does not want to sign one more centre-back this summer, even if Maguire decides to pack his bags at Leicester.
"Harry's a top-quality player and no-one has come near the valuation to tempt the club to sell", Rodgers said, speaking after Leicester's 1-0 friendly win over Scunthorpe United. "He's been absolutely brilliant, I have to add, because I've been in a similar situation a number of times and it can be very hard for players, but he's a special guy".
Reigning Premier League champions Manchester City are also thought to be keeping an eye on the situation as they look to replace departed club legend Vincent Kompany and there has been renewed gossip about interest from the Etihad Stadium this week.
"I think he's a very good central defender and he has proven himself at the global level as well, but a part of me thought that they would go overseas to fill that role".
Williamson hails NZ after World Cup stunner
England were all out for 241 on the last ball of the 50th over, chasing New Zealand's 241 for eight. The value of the Black Caps' pragmatism in reaching 241-8 was shown when England came to bat.
United are hoping to bring in a top-level centre-back before the transfer window shuts next month and PA understands the England global is in the Old Trafford giants' sights.
"It's a hard one because I think the back four is certainly somewhere that they have had issues, but he had a really good season previous year and hopefully he can replicate that", he added.
"He came here to play and you can see the quality he has in those 45 minutes".
"I've been in this position a number of times and it's never easy but he's taken part in everything and hasn't showed anything other than sheer professionalism".
"The simplicity is that there is a valuation that hasn't been met yet and until that happens he is very much focused on being a Leicester player", Rodgers is quoted as saying by Sky Sports. "There's obviously been a lot of speculation surrounding him but we're relaxed about it".