Walker sat out the training session because of a back problem picked up during the FA Cup final on Saturday. He was substituted in the final minute of the 2-1 win over Manchester United at Wembley and faces a race against time to prove his fitness ahead of the Champions League final against Inter in Istanbul on Saturday.
"He had a disturbance in his back," Pep Guardiola told a news conference on Tuesday. "Yesterday [Monday] he was not good and today he was a little bit better. We didn't want to take a risk and we will see what happens in the next days."
City's clash against Inter will be the Premier League champions' first appearance in the Champions League final since losing 1-0 to Chelsea in 2021.
Guardiola fielded a suprising lineup that day, starting the match without a recognised holding midfielder -- a decision which back-fired as Kai Havertz scored the only goal of the game.
When asked whether he still blamed himself for the defeat, Guardiola said: "It was a gameplan like it will be next Saturday.
"If I tell you privately the reason why I took the decision in that moment you could say it was right but it is simple: If I lose, I am wrong, if I win I am right.
"You have to accept that in this business. It was a tight game and in many things we were better than them but we lost. Would I do something different now? Maybe but that doesn't count."
Guardiola has not won the Champions League since his time in charge of Barcelona while City are looking for their first ever success in the competition.
City have won five of the last six Premier League titles and have already won the league and cup double this season, but Guardiola accepts a lot still rests on the result in Istanbul.
"Sooner or later we have to win in Europe to go to another level," he said.