Speaking in the second part of his press conference on Tuesday morning, Jose said that the Reds may be without the former England international.
Fellow defenders Chris Smalling and Eric Bailly may also miss out, while Antonio Valencia and Luke Shaw could be doubts.
The boss admitted that it will be a race against time for any of them recover to face Unai Emery’s Gunners.
If our game was today, I’d say Jones is not playing, Smalling is not playing and Bailly is not playing but we will have to wait,Jose said.
Valencia is not playing. Shaw is a doubt. Darmian is back, but I have to wait. Of course, Lindelof is out of the question.
Saturday’s 2-2 draw on the south coast was Jones’ second Premier League appearance of the season and only his fourth in all competitions, having suffered with a hamstring problem at the beginning of the campaign.
The defender was lined up alongside Nemanja Matic and Scott McTominay in the heart of the Reds’ defence during the match at St Mary’s.
When the manager spoke to MUTV earlier on Tuesday, he highlighted how United’s back line has been beset with injuries.
Against Southampton, three hours before the game I didn’t know the team that is going to play, so nobody knew the team and ourselves, we didn’t know, he said.
We were waiting and waiting and waiting to see who could, who couldn’t, and I think we are going to be in a similar situation this time.
United will aim to close the gap on fourth-placed Arsenal to five points when Unai Emery’s side arrive at the Theatre of Dreams on Wednesday night.