"I hope he does it. It couldn't happen to a better person," the 11-times former grand slam champion told Reuters in an interview on Tuesday.
"I think he will win his 11th grand slam title and if he keeps his motivation and remains injury-free, he will become the tennis player with the most wins ever in grand slams."
Borg, 51, won every Wimbledon from 1976 to 1980 before losing to American John McEnroe in the 1981 final.
Federer, Wimbledon champion for the last four years, could match that feat this year at the All England Club where he had a walkover into the quarter-finals after German Tommy pulled out with an abdominal muscle injury.
In the final eight, he faces former French Open champion Juan Carlos Ferrero.
Federer, 25, first hit the headlines at Wimbledon in 2001 by wrecking Pete Sampras's dream of equalling Borg's five-in-a- row, beating the American in five sets in the fourth round.
The Swiss went on to lose to Britain's Tim Henman.
He has since amassed 10 grand slam titles, including his first Wimbledon in 2003.
Sampras still holds the record of 14 grand slam singles titles as well as the record of seven Wimbledon titles, won from 1993 to 1995 and 1997 to 2000.
Borg believes Federer could match Sampras.
"He is incredibly professional in what he does and he keeps his feet firmly on the ground. He certainly sets an example in tennis," Borg said.
"If Roger carries on at the same pace he has kept up for the last few years, he will become the absolute greatest ever to have played tennis."
Asked about suggestions that Borg should present the trophy after the final this year, the Swede said: "I think we should stick to tradition and let the royal family carry on handing it over."
