The former world number one and self-proclaimed "hard-court specialist" reached the semi-finals of the tournament last year for his best result at the All England Club where he was dispatched in straight sets by eventual champion Carlos Alcaraz.
"I think quarters, semis for him are what I would expect," McEnroe, a former player and current ESPN broadcaster, told reporters on a call.
"He's a good grass-court player. In my view, he's not a great grass-court player. By the way, there are very few great grass-court players."
Those select players are also the top three in the world - number one Jannik Sinner, seven-time champion Novak Djokovic, and defending champion Alcaraz, McEnroe said.
What they possess that the likes of Medvedev, Stefanos Tsitsipas, Alexander Zverev and Taylor Fritz lack is the dynamic shotmaking and speed that can keep opponents off balance.
"I think Medvedev doesn't have enough variety in his game," McEnroe said.
"(Sinner) has added a little more variety - the ability to chip, the ability to come forward, play the dropshot, play with a little more finesse."
Medvedev, ranked number five in the world, had a hot start to the year, reaching the Australian Open and Indian Wells finals, as well as the semis in Miami, all hard-court tournaments.
But he has cooled off recently, falling in the fourth round of the French Open and losing on the grass courts at the Halle Open to world number 33 Zhang Zhizhen in last 16.
"Hard courts is still his best surface. I put him as a guy that can win the US Open or Australia," McEnroe said.
"He'll be solid, but if you remember last year, he just got absolutely destroyed in that semi-final match," he said of Medvedev's 6-3, 6-3, 6-3 drubbing by Alcaraz.
"I just think for him to go up against one of those two guys, or if Novak were healthy, that's a match he can't win on grass if those guys are at their best."
Three-time Wimbledon champion and ESPN broadcaster Chris Evert concurred.
"I think quarter-finalist," she said.
"This all depends on the draw, who matches up well to whom. But I wouldn't put him in the top four or five right now."
