The Spain international spent four seasons at Old Trafford before joining Barça in 2008 and has kept a close eye on his former club.
United made Maguire the most expensive defender ever this summer when they paid Leicester City £80 million for his services, and Pique believes the England international could prove to be good value for money.
"It happened before with (Virgil) Van Dijk and before about 10 years ago with Rio Ferdinand," Pique told the Express.
"Culturally they invest a lot in good defenders and Harry Maguire is a great defender. I hope that they can be at the top again.
"Manchester United in the last few years they have been fighting to qualify for the Champions League but they have to be trying to win the Premier League. I hope with this signing they can return to the top."
Pique played alongside current Red Devils boss Ole Gunnar Solskjaer during his time in Manchester and has been impressed by the Norwegian’s work so far.
"I saw him last year in the Champions League tie and I think he's a great lad and a great guy," he said.
"He is doing a very good job at Manchester United, let's see this season how it goes for him and the team."
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