Novak Djokovic, 31, dropped just five games against Zverev, the 21-year-old German who is leading the supposed next generation of ATP Tour stars at the Tour Finals on Wednesday.
Zverev, who won his opening group game against Marin Cilic, now needs to beat John Isner to guarantee qualification for the semis but Antic is expecting big things regardless of what happens this week.
He told the Tennis Podcast: “We haven’t had the situation with a top German for a long time. Rainer Schuettler, Tommy Haas, Nicolas Kiefer – they were all top 10 players but Zverev is the first one to be twice at the season-ending tournament.
“He was good last year and now he is still good. He didn’t drop in the ranking so that is a special thing about him in Germany of course.
“Germany needs a good tennis player and of course we met many, many times and I think he could be No.1.”
Although Antic has one problem when it comes to the hard-hitting German – getting an interview.
On what he’s like away from court, he explained: “He’s actually a nice guy. Sometimes it’s a bit difficult with the team because he moved so quick in the rankings so there’s a lot of stuff that people want from him.
“Even for people who are closer to him, sometimes it’s tough to get an interview.”
Big things are expected for Zverev but he is still yet to have caught the public’s eye like the greats before him.
“There is support for Zverev in Germany but you can’t compare it to Boris Becker or Michael Stich,” Antic said.
“He is a bit further away – or seems to be – because he trained in Tampa, Florida, he lives in Monte Carlo, he has the Russian origins. I think people still have to learn to get to know him a bit better.
“He’s in the process to become more well known in Germany but now he’s not there where he could be with No.5 ranking or No.4 or No.3 in the world – he could be more accepted.”
Following Djokovic’s 6-4 6-1 win, the seventh straight-sets singles result in seven matches, Djokovic backed the new guard to come good.
He insisted: “I think there is a lot of quality in the new generation.
“Zverev is obviously the leader of that next generation. He has proven himself, established himself as a top player. He has won many Masters 1000 events already, I think three in his career, which is quite impressive.
“You have to give him credit for that, for qualifying for World Tour Finals two years in a row. Then you have players like (Karen) Khachanov, of course, (Stefanos) Tsitsipas, (Borna) Coric. I think tennis is in good hands.
“At the same time I think us older guys, we’re still obviously working hard, and working smart, and trying to get the most out of what we have in ourselves left.
“How long that’s going to go on for, we don’t know.”