Lenglet was one of the last signings of Monchi's tenure as Sevilla's sporting director, joining in a reported €4.5 million deal from French side Nancy, whom he captained despite his tender age.
The former France Under-21 international's ability on the ball and passing range in particular have caught the eye, while he has often displayed a talent for reading the play well, as exhibited by his strong performances against the physical threat of Manchester United's Romelu Lukaku in the Champions League last 16.
Barcelona, who Sevilla face in Saturday's Copa del Rey final, are said to have been keeping tabs on Lenglet since his early days in La Liga and have been linked with a move at the end of the season.
"Lenglet is a champion, both in his head and on the pitch," Montella said of the Frenchman at a news conference ahead of Tuesday's league meeting with Deportivo La Coruna.
"He could play in a big team like Barcelona in the future, but I hope he stays at Sevilla for some years."
Lenglet is not the only man at Sevilla whose future is unclear, as Montella himself is under a bit of pressure after a poor run of five games without a win in La Liga, which has seen bitter rivals Real Betis move above them.
Montella took over from Eduardo Berizzo in December and, although he presided over the impressive 2-1 aggregate win over United, some sections of the club's supporters doubt he is the right man to lead them next term.
"I'm happy in Sevilla," he said. "I have a contract next year, although it's not something I think about.
"I focus on day-to-day work. I know there are some conditions for the extension of the contract, but I do not think about that. Of course I would like to be here next year.
"I do not like to talk about myself. I am very critical of myself and I know there are many things that can be improved.
"We work for it, but it is not easy to do it while La Liga is in progress. We need time and it's complicated."