But Liverpool legend Phil Thompson has advised the Reds to make a move for Maguire to stop their rivals strengthening.
“I like what Jurgen Klopp has done by trying to strengthen the players behind the front three and get more goals from that area,” Thompson told Sky Sports.
“That part of the team is where you win titles and Fabinho, [Xherdan] Shaqiri and [Naby] Keita can provide that additional firepower. [Adam] 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.”
Maguire was instrumental for England at the World Cup (Image: GETTY)
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Liverpool boss Jurgen Klopp is still in the market for more additions, although he would like to offload some fringe players first.
"I can't kill your D-Day where people sit in front of the TV and watch,” Klopp said.
"If any player from my team is available then in every other situation in my life as a manager I would have bought any of them.
"They are all fantastic boys. In this moment the squad is too big, that's true. But it's not that we give them away for free.
“Liverpool is strong enough to keep all these players and then we deal with that. We aren't here to make any other teams stronger."