Leicester are aware of United's interest and "will improve Maguire's wages to around £75,000 in a bid to tie him down for another season", but that weekly sum might not be enough to fight off United's financial muscle.
Manchester United have not hit top gear on their pre-season tour of the United States but manager Jose Mourinho has said he is not anxious as a majority of his first team players are yet to rejoin the squad following the World Cup.
Leicester boss Claude Puel has commenced behind the scene moves for potential replacement with the likes of Barcelona's Yerry Mina and Chelsea's Gary Cahill on his wish list.
Undermanned following the World Cup, United were disjointed and void of creativity as they fired a blank against the MLS strugglers.
Mourinho, the United manager, is thought to be happy with his options at full back and wants to sign Maguire, the centre back, who is valued at more than £50 million after his impressive performances with England at the World Cup this summer.
Leicester will hope to fend off United's interest until then with the transfer window closing on August 9.
However, Mourinho has waved away speculation that the 22-year-old could part ways with the club, as he insists the winger's future does not lie in his own hands.