McArthur has been suffering from a dead leg after picking up the knock during a training session before the clash against Tottenham earlier this month.
The Scotland international had been hoped to recover in time to face West Brom at the weekend, but he failed to recover.
And now the Latics boss is sweating over the midfielder ahead of the trip to Anfield.
"It's hard to tell, because we expected James to be fully fit for the West Brom game and it was disappointing to see him miss out," Martinez told the Evening Post.
"His dead leg is worse than we originally thought, and already we are looking at Thursday or probably Friday before we'll know if he'll be okay for Liverpool."