Palmer, who suffered a groin injury in August before returning with back-to-back goals against Brentford and Bayern Munich, was nearing his comeback, but an accident at home delayed his return.
The 23-year-old England international stubbed his toe on a door during the night, resulting in a fracture.
"Cole is wearing a (protective) boot," Maresca told reporters.
"We don't know when he will be back but for sure it will be soon. He's already on the pitch, he's already touching the ball and the feeling (for him) is good.
"I don't think he will be available for these two games (Barca and Arsenal), but he is doing well."
Chelsea sit six points behind leaders Arsenal in the league, with 23 points from 12 matches. The sides meet in a London derby at Stamford Bridge on Sunday.
Maresca, however, was not looking too far ahead, with five-time Champions League winners Barcelona up next.
"It's a big week, but at the end of this week. We have Leeds away, Bournemouth away, Atalanta away," the Italian said. "Every game is three points.
"Barcelona tomorrow and Arsenal on Sunday are important for different reasons, but it's important for us to go game by game."
Lewandowski and Lamine threat
Barca, second in LaLiga, bring firepower in abundance to Stamford Bridge, with Robert Lewandowski leading the line. The 37-year-old Polish striker has netted eight goals in LaLiga this season, second only to Real Madrid's Kylian Mbappe, who has 13.
Barca teenager Lamine Yamal, second in the LaLiga assist charts with six, also poses a significant threat.
"For sure he (Lewandowski) is a fantastic player. He has shown all his life that he does the most important thing in football, score goals. We are going to try and defend as a team, be aggressive, like we always defend," Maresca said.
"But they have so many players; Yamal, Fermin Lopez, Frenkie de Jong."
