Maguire starred for England at the World Cup this summer and his form attracted Manchester United to make a move.
However, a deal failed to materialise as United refused to meet Leicester’s asking price, reported to be more than the £75million Liverpool paid Southampton for Virgil van Dijk in January.
Maguire joined Leicester in the summer of 2017 from Hull for a fee that could rise to £17m.
And Morgan hopes his centre-back partner stays at Leicester long term and fulfils his potential.
“Ever since he’s come he’s been a revelation,” Morgan told Sky Sports.
“I think he’s settled in so well and for me, he’s just got better and better.
“I think more his confidence has grew, he’s obviously taken the step into the England setup.
“He looks like he has been part of that setup for years.
“The confidence he has on the ball, the way he starts attacks. He’s got a lot of attributes for a big central defender.
“He’s had a lot of attention over him over the summer with possible going to other teams, but I’m glad he stayed here.
“I think it’s very important (that he stayed).
“His first season was last season and he had a fantastic season, got the player of the year awards and rightly deserved that as well.
“I just want to see him impress, continue to improve and be the great player I know he’s going to become.”
Maguire is in the England squad for the upcoming Nations League matches against Spain and Switzerland.
He has started all four of Leicester‘s Premier League games so far this season.
The Foxes sit eighth in the table with two wins and two draws.
Bournemouth are next up for Claude Puel’s side after the international break.