Maguire was a rock at the back for England during the World Cup, playing a crucial role as the Three Lions made it all the way to the semi finals.
His performances caught the attention of United boss Jose Mourinho, who is keen to sign the defender. The only problem for the Red Devils being that Leicester reportedly value Maguire at £65m.
However, speaking for Sky Sports, former European Cup winner Phil Thompson has called upon Liverpool to snatch the 25-year-old from United's grasp.
Thompson said: ''I like what Jurgen Klopp has done by trying to strengthen the players behind the front three and get more goals from that area. That point of the team is where you win titles and Fabinho, Shaqiri and Keita can provide that additional firepower. Lallana is also back.
''With one more centre back, Liverpool can be a real force; I'd be looking at snatching Harry Maguire from under Manchester United's noses.''
However, with just a few days left in the transfer window, it appears that Maguire's destiny is to stay at the King Power Stadium, for another season at least. Leicester are not willing to sell Maguire, unless they can definitely get in a replacement, something that is appearing unlikely given the time constraints.
In regards to Thompson's view that Liverpool should sign Maguire, as much as the Reds would like to steal a player from United's grasp, it is unlikely to happen.
Liverpool have had a record breaking transfer window and appear to have finished their transfer dealings, and may not even be able to afford another huge signing.
It should be remembered that Virgil van Dijk and Dejan Lovren formed an effective partnership at the end of last season, and Klopp appears to be sticking with them as his centre back pairing.