City begin their European Cup defence against Red Star Belgrade in Group G on Tuesday but may be without the trio again.
"We'll see step by step," Guardiola told reporters on Friday. "The injury for Jack is muscular but he has an incredible knock for his knee and the damage is there.
"John is better but still has issues. (Kovacic) has something also muscular. It's not a big issue but also he is out."
Guardiola's personal return to the bench after missing two games for emergency back surgery was a bit of good news amid his squad's injury troubles.
"Thank you for asking, I think every week will be better," the Spaniard said. "It was strange (missing the games), but it was OK."
Defender Kyle Walker signed a two-year extension on his contract this week amid rumours of a move to Bayern Munich, and Guardiola praised the 33-year-old as a "really important figure" for the team.
"It's great that he decided to stay. His mind is here on the pitch, loving football," Guardiola said. "Few players have genetics like him. He has stability in his life and (his age) won't be a problem."
Walker was left out of City's squad for the Champions League final after he started both legs of the semi-final.
"I was sad that he didn't get to play in the Champions League final, but look how good his response has been since then," Guardiola said.
Walker has mentioned he hopes to be captain and Guardiola said a vote will be taken in the next few days.
While City are the only team in the top flight with a 100% record so far, Guardiola insisted the season really only starts now.
"The season always I believe starts right now, after the first international break, the transfer window is over, the kids back to school," he said.
"The real season I would say starts right now for a lot of competition, the Champions League, Carabao (League) Cup and the Premier League, so that's why, yeah, go for it."
West Ham are fourth in the standings with 10 points.
