The 35-year-old defender signed a one-year contract with Sunderland earlier this year.
Reveillere originally joined the club as a means to work back to full fitness, but he signed a one-year deal in October with the Black Cats in the midst of an injury crisis.
The French international has since turned out four times for Gus Poyet’s side, and he has shown his experience in a number of impressive displays. Regularly filling in at left-back due to the injured Patrick van Aanholt, the club have yet to lose a game in which the 35-year-old has played, with one victory - a 3-1 win over Crystal Palace - and three draws heading into a tie with Manchester City on Wednesday.
His most recent appearance was on Saturday, as the Black Cats fought to a 0-0 draw with Premier League champions elect Chelsea, and he once again showed his talents as the Wearside club became the first team to prevent the Blues scoring this season. His introduction into the team has been well received at the Stadium of Light, and with the club progressing well in the top flight, the former Lyon full-back has become something of a fan favourite - a feeling that is mutual.
Speaking to the Chronicle, Reveillere revealed his pleasure to be turning out on a week-by-week basis for the Black Cats.
“I’m just looking to make the most of each game as it comes,” the Frenchman said. “That’s what you do when you get to 35!
“I’m really enjoying the Premier League.
“I really like the club, the players, the stadium and the life over here.”
While he is in the swan song of his career, and he is likely to feature less regularly as age catches up with him, Reveillere did admit that he has thought about extending his stay on Wearside, although he stressed that the club had not offered him a new contract.
The 20-capped international continued: “I haven’t thought that far ahead yet.
“If Sunderland offer another contract, then we will see.
“So if there was a chance to stay here longer, then why not?”