Federer became the oldest ever world No 1 earlier this year after winning the Australian Open.
However, arch-rival Rafael Nadal has since leapfrogged the Swiss star back to the top of the rankings.
Thiem, who many expect to be Nadal’s heir on clay, does not think the pair, nor Novak Djokovic, will continue to rule the world for too much longer.
Instead, the Austrian believes they will faint into the shadows of Alexander Zverev and Nick Kyrgios, who are expected to be the next big stars on the tour.
“Federer World No 1 in 2020? I don’t think so,” Thiem told GQ Magazine.
“He will be 39. Nick Kyrgios, Alexander Zverev will be even more at the top.
“But [Andy] Murray, Djokovic and Nadal will be 33-34, they will be there.”
Thiem is hoping to help his national side to gold in Tokyo in a competition which could well be one of Federer’s last.
And West Ham United striker Marko Arnautovic has tipped his fellow countryman to also challenge near the top of the rankings.
“Dominic has done a great job and he is still young,” Arnautovic said.
“He’s done a lot of good things and is now in the top ten in the world.
“He’s a very good player but he’s still got a long way to go because he’s young and I think, if he keeps working hard, hopefully he’s going to be the top one.
“It’s not normal that we can do this because Dominic has a game tonight and he’s come out with his partner to play football and enjoy some time.
“Now it’s time for him to go back, concentrate, take a rest and beat this guy up!”