Manchester United had made Maguire a top target in the summer after watching him help England reach the World Cup semi-finals.
The Red Devils are said to have had two bids turned down by Leicester, the second believed to be worth around ÂŁ65m.
Puel believes the 25-year-old announced himself as “one of the best” centre-halves in the world during his time in Russia.
And the Frenchman admitted he expected other clubs to want Maguire on the back of his displays this summer.
â€śIt’s a difficulty but my first feeling was that it is amazing for this player to show their qualityâ€ť
“Yes, of course I did,â€ť Puel said.
â€śIt’s a difficulty but my first feeling was that it is amazing for this player to show their quality and it’s good publicity for Leicester.
“When he came back after the World Cup he could maybe feel almost cocky.
â€śHe could have been, but he’s not. He came back with humility and with desire and will.
“He is one of the best, there are a lot of good players from this World Cup, but he showed a good attitude like the man he is.”
Maguire is thought to have been Jose Mourinhoâ€™s No.1 target as United looked to sign a central defender ahead of last nightâ€™s transfer deadline.
The two sides go head-to-head this evening at Old Trafford to kick-start the Premier League season.
And Puel outlined some of the qualities he thought made Maguire of interest to United.
He added: “I was happy with the progress of Harry in the second half of last season.
â€śHe played with consistency and good progress, was strong in his defensive aspect and with quality to start with the ball.
“I like a player with a possibility to start from the back and Harry is this player. He showed this in the national team.
“He’s a fantastic player and a fantastic man because he listens a lot, he wants to improve, he has a good personality and character but always with good respect for the staff and his team-mates.”