The 17-year-old Belgian has been subject of enquiries from City, but was invited for a two-day trial at Goodison Park according to Hans Galje, the caretaker manager of Lestienne's current club Excelsior Mouscron.
Lestienne has shone in the Belgian league, after coming through his club's youth system, sparking interest from City.
Galje was defiant despite Everton's interest, saying: "I know Lestienne has been asked to come and visit Everton for a couple of days, but they can take a place in the waiting room. There are an incredible amount of clubs interested in this guy. I understand Maxime won't leave Mouscron soon.
"The invitation of Everton is to show him the stadium and that's not that strange. But first Maxime wants to take a look and then Mouscron will have to be asked permission for that to happen."