Mendy missed the defeat to Wolves with a hamstring injury but is closing in on a return, while Sergio Aguero should be available after escaping unhurt from a minor car crash in Manchester on Wednesday morning.
"Some of them are back," Guardiola told a news conference on Friday. "Kevin is back, John has trained well the last two days. Mendy a little later but he's back."
City will aim to get back on track against Palace -- who are sixth in the table after eight games -- after defeat to Wolves left Guardiola's side eight points behind leaders Liverpool.
City and Liverpool have become embroiled in a fixture row after Premier League released a Christmas schedule that appears to favour Jurgen Klopp's team.
City will have less than 48 hours to prepare for their home game with Sheffield United at 6 p.m. on Dec. 29 after playing Wolves at Molineux at 7.45 p.m. on Dec. 27.
Liverpool, meanwhile, have an extra 24 hours to rest between games against Leicester City on Boxing Day and Wolves on Dec. 29.
"It's what it is," Guardiola added. "Since I came here every season it's the same. The broadcasters are the bosses, it's not about us.
"I love to play Boxing Day, families go to the stadiums, the players travel but the system does not protect the players too much.
"Maybe the broadcasters are fans for some clubs. We have meetings with Premier League, managers, UEFA, they are so glad, nice pictures, it doesn't matter -- we have to play."
Palace are just two points behind City after an impressive start to the season that has pushed Roy Hodgson's team into the European places.
Palace have enjoyed success against City, recording a 3-2 win at the Etihad Stadium and earning a 0-0 draw at Selhurst Park in December 2017.
"Playing against Crystal Palace is always difficult, no matter if we won in our last game there at Selhurst Park or not," said striker Gabriel Jesus.
"It was a very difficult game, as usual. We are going to prepare the game the best we can to try to give a good performance and win.
"Last season, we lost our game against them at home and we won away. You can see how curious football is. No matter what our injuries are, I think we can win there. But I'm sure it's going to be a very difficult game."