Liverpool are thought to be on the lookout for further defensive reinforcements during the final month of the transfer window and have been credited with an interest in Maguire for a number of years.
The 25-year-old's performances for England during the World Cup have stirred up speculation that a move to a top-four club could be imminent, and Thompson believes that he would be a valuable addition to the Liverpool team.
"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," Thompson told the Liverpool Echo.
"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.
"Harry has been one of the best defenders in the World Cup and he certainly fits Liverpool's philosophy. I can't speak more highly of him. No disrespect to Leicester but I can't see him being there come the end of the transfer window. I think he would have been £50m before the World Cup and probably a bit more now. But I think he would be worth it. Big clubs will be after him and I'd like to think that Liverpool would be at the forefront.
"Harry would be an upgrade [on Dejan Lovren]. He's like an English version of [Virgil] Van Dijk. Harry is probably even more physical than Van Dijk which is another plus and I'd see them as a great combination. He would give us that extra solidity back there. It would be another statement. They would be our centre-back combination for years to come."
Maguire only joined Leicester last summer, making 44 appearances for the Foxes during the 2017-18 campaign.