Coach Mike Mularkey said he's hopeful that Jones-Drew will be able to play in next weekend's season finale at Tennessee.
The Week 16 game will mark the ninth straight that Jones-Drew, the NFL's leading rusher last season, has missed. It opens the door for a number of reserve running backs to take on a starting role.
The Patriots have been preparing as if Jones-Drew was going to play and made it abundantly clear how much they respect his contributions.
Said coach Bill Belichick of Jones-Drew: "He brings everything. He has great balance, vision, power for his size. He's a thick guy, hard to put on the ground. [He] sees the holes well, runs with good power, has good speed, catches the ball well out of the backfield, he's dangerous on the check-downs and flare routes, screens, things like that. He's very good in the line of scrimmage on the inside runs, very good on the outside runs. He's a tough guy to handle in space. He does everything well."
Montell Owens, a seventh-year player out of Maine, started for the Jaguars in Week 15.
Jacksonville claimed running back Jonathan Grimes off waivers from Houston on Friday.
Grimes played in nine games this season, six with the Texans and three with the New York Jets. He had two carries for 6 yards with the Jets.
An undrafted rookie from William and Mary, Grimes had a team-best 130 yards rushing for Houston in the preseason. He was waived in final cuts and signed to the practice squad. The Jets claimed him in September and waived him Oct. 30. The Texans claimed him the following day and parted ways with him Thursday.
Information from The Associated Press was used in this report.