The Sheffield-born centre back has enjoyed a terrific World Cup campaign with England this summer and recently scored the opening goal in the Three Lions' win over Sweden to reach the semi finals of the tournament.
And among the defender's growing list of admirers is Thompson, who made 340 league appearances for Liverpool between 1971 and 1984.
Speaking to the Liverpool Echo, Thompson said: “I’ve been a big fan of Harry Maguire since his days at Hull City.
“Since then he’s got better and better. He’s had a fantastic World Cup so far.
“I was saying long before the tournament started that he has all the attributes needed to be a Liverpool player.
“He’s big, he’s strong and positionally he’s very good whether as a two or a three at the back.
“He’s a lot quicker than people give him credit for. He dominates in the air and that’s a major asset both defensively and offensively.
“He’s also very comfortable on the ball. He’s better than John Stones when it comes to passing it out from the back.”
After impressing for the Tigers despite their relegation from the Premier League in 2017, Maguire was then snapped up by Leicester for a fee of £12m, becoming one of the Foxes' standout players in the 2017/18 season to earn a place in Gareth Southgate's 23-man squad for the World Cup.
Maguire has featured in every game for England in Russia, forming a strong back 3 alongside Manchester City pair John Stones and Kyle Walker.