Head coach Enzo Maresca labeled the challenge from Manchester United defender Lisandro Martinez on the 22-year-old as "reckless," and expressed concerns that the England international may be sidelined for the upcoming London derby after Sunday's 1-1 draw.
Palmer has not trained since the incident, which occurred in stoppage time and earned Martinez a yellow card, and he is not eligible for Thursday's Conference League game at home to FC Noah.
"He didn't train (Tuesday), we'll see today if he is able to train with us," said Maresca.
"Hopefully he'll be ready (for Arsenal) but we need to wait and see, then decide."
TrendingAsked whether there was a chance Palmer could miss Sunday's game at Stamford Bridge, he said: "Yeah, for sure. He didn't train the last two days. The tackle it's quite clear was not a normal one. But hopefully he can be back."
Palmer has been the outstanding player during Maresca's first four months in charge, scoring seven goals and further establishing himself as the team's creative heartbeat.
Maresca is likely to use Thursday's game against Armenian side Noah to assess alternatives with wholesale changes to the line-up expected.
Jadon Sancho is not among those available after he missed the game at Old Trafford through illness and has since picked up a knock, though Joao Felix is a player that will be hopeful of using the match to stake a claim to a starting berth against Arsenal.
The £42m summer signing is yet to start in the league and was not called upon from the bench against United.
"I feel a shame about Joao," said Maresca.
"I would like to give him more minutes in the Premier League but we need defensive balance and we cannot play with Joao, Cole, Christo (Christopher Nkunku).
"I'd like to put them all on the pitch but then you have to also defend. You need the right balance between the two phases, attacking and defending.
"This is the only reason. I don't have any doubt that if (Felix) keeps working well he's going to find his moment in the Premier League."
Felix is one of several big-money buys struggling for minutes in the league under Maresca.
Enzo Fernandez, signed for £106m less than two years ago, has been benched for the last three games while £55m arrival Nkunku has played second fiddle up front to Nicolas Jackson.
The France international is the club's top scorer with eight, having made the most of starts in the Conference League and Carabao Cup, underscoring Maresca's difficulty in spreading starts amongst his 24-man squad.
"Every time (Nkunku) plays, he scores," said Maresca.
"He was probably our best player in pre-season. He played as an attacking midfielder, now we are using him as a nine. We all know it's not his position, he's more second striker playing between the lines.
"But I try to find solutions and balance. I can understand that not all of them can be in their position, they have to adapt a bit. They all deserve more chances in the Premier League but we have more players that deserve that."