The Chelsea skipper, who has not played since early September, was unable to train on Thursday after aggravating the injury but Conte said the 35-year-old would be ready for the clash against Jose Mourinho's United.
"John is in good shape," Conte told a news conference. "He trained with the team (on Friday). He solved his problem with his ankle. He's available for the game."
Terry has been out of action for five weeks since suffering the injury against Swansea City, although he did make the bench for last weekend's 3-0 defeat of champions Leicester City.
Mourinho's return to Stamford Bridge, almost a year after he was sacked by the club for a second time following a dreadful start to the defence of their Premier league title, adds extra spice to the fixture this season.
The Portuguese is Chelsea's most successful manager, having won three league titles in two spells in charge, but Conte is trying to build his own legacy at Stamford Bridge and will hope to make it an unhappy homecoming for Mourinho.
"I want to see progress on Sunday compared with the Liverpool and Arsenal games and I am confident I will," Conte said. "It will be a tactical game on Sunday but he the fans have a big part to play and can be an advantage.
"I have great respect for Mourinho," he added. "He deserves a good reception. He was an important man for Chelsea and wrote part of the club's story."
(Reporting by Martyn Herman; Editing by Toby Davis)
