Nineteen-year-old Alcaraz broke through to record his maiden Grand Slam win at the recent US Open, resulting in him becoming the youngest world number one in tennis history.
There seems to be no limit to the young Spaniard's potential, with many already tipping him to rival the likes of Nadal (22), Djokovic (21) and Federer (20) when it comes to career Grand Slam victories.
But former Wimbledon champion Bartoli reckons people are underestimating just how unlikely the achievements of tennis' big three are.
For a long time, Pete Sampras' 14 slams were seen as an insurmountable target, and even matching his record would still be a massive achievement for any player.
"I think there is absolutely zero chance that anyone ever - not only Carlos Alcaraz - will reach the bar of 20 or more [Grand Slams]," 2013 Wimbledon champion Bartoli told Tennis Majors' Match Points talk show.
"I think what the three guys have been achieving over those years is out of normality and I don't think anyone can replicate it.
"Carlos's achievement at the US Open was amazing, but I don't think it's realistic to set the bar for him at 20 and over."
Listening to Alcaraz' coach Juan Carlos Ferrero talk, however, his young protege is only just getting started and still has massive room for improvement.
"I think he's on 60% of his game. He can improve a lot of things. He knows and I know that we have to keep working," said Ferrero, himself a former world number one.
"Once you get to the No 1, it's not done and you go. You have to keep working, keep playing at a huge level on that tournaments to keep winning. He knows that and I know that. I'm going to be very close to him to remind him."
Having played at the highest level himself, however, Ferrero does acknowledge that equalling the achievements of the big three will be a very difficult task indeed.
"I have the goal to put him on the high level of tennis," he said.
"Of course, I think it's going to be very, very difficult to achieve what they have done on tennis. We're talking about 22 Grand Slams. He has only one. Is a long way still to go.
"But who knows? I think he has all the tennis and potential to be one of the best. All we have to do is try it."