Jones-Drew hasn't played since Week 7 against the Oakland Raiders. The franchise running back is battling a foot injury. His return is still unknown.
"We still think he has a chance to come back for a few games," Mularkey told reporters at his Monday press conference.
Jones-Drew has been one of the NFL's best running backs for the last four seasons, so his absence has been crucial for the lackluster Jaguars. Jacksonville is 2-9 this season and sits in last place in the AFC South.
In six games this season, Jones-Drew has racked up 414 yards and a touchdown on 86 carries.
In the previous three seasons, Jones-Drew rushed for at least 1,300 yards. In 2011 he led the NFL with 1,606 rushing yards and 100.4 yards per game.
In 2009, Jones-Drew had a career-high 15 touchdowns on the ground.
The Jaguars visit the Bills (4-7) on Sunday at 1 p.m.