Boss Roy Hodgson is definitely without full-back Ward due to a "serious knee injury" and could have another casualty ahead of the Clarets clash.
Ex-Chelsea defender Cahill trained on his own on Thursday and had an ice pack on his knee afterwards.
Palace will now assess the centre-back on Friday to decide whether he can rejoin the main group for training at Beckenham before they travel to Turf Moor.
Hodgson will hope Cahill is fit enough to play, but will definitely be missing Ward and does not expect him to feature again until 2020 after suffering the problem going in for a challenge with Liverpool's Divock Origi.
"You know how doctors and medical staff are, they are reluctant to put a date because they are frightened you are going to come back after a period of time and demand the player returns," Hodgson said.
"But it is a serious knee injury in the sense it will keep him off for a number of weeks rather than a number of days. I can't tell you exactly what the timescale is, but it will be a considerable amount of time."
In Ward's absence, Martin Kelly - who worked with Hodgson at Liverpool - is likely to earn a recall and make his first start since October 5.
Once an England international, the 29-year-old is comfortable playing at the heart of defence or on the right, which is where he will line up this weekend.
For the Clarets, Ashley Westwood will miss the game through suspension and boss Sean Dyche has confirmed that Danny Drinkwater could be set for a surprise return to the side.
The midfielder, who is on loan from Chelsea, has had a troubled time since arriving from Stamford Bridge, but could be given a rare chance to shine against Palace after impressing in training.