Jones, 25, was forced off just 23 minutes into United's 2-1 defeat at Huddersfield Town on Saturday (20 October) due to a quadriceps injury and was replaced by summer signing Victor Lindelof.
The England international was fit enough to make the journey to south Wales for his side's Carabao Cup fourth round clash against Swansea City on Tuesday however and was named on the bench as United saw out a comfortable 2-0 win courtesy of a brace from Jesse Lingard.
Chris Smalling, Axel Tuanzebe and Lindelof operated in a back three at the Liberty Stadium but Mourinho is confident Jones will be ready to return on Saturday with United hoping to quell the threat of the league's leading goal scorer Harry Kane.
When asked for a squad injury update, Mourinho told Sky Sports: "I think Jones will be [back]. Today he was on the bench and he told me that in case I needed [to bring him on] he would be ready. So I believe he will be even better for Saturday. Apart from that, I have no news and when I have no news I have no hopes."
Mourinho's comments would suggest Bailly will not be in contention to return on Saturday. The Ivory Coast international returned from the recent international break with an unspecified knock that has ruled him out of games against Liverpool, Benfica and Huddersfield.
The former Villarreal defender returned to training this week but could still face a battle to be ready in time for the visit of Mauricio Pochettino's side.
United also remain without the option of Marcos Rojo at the back, although the Argentina international is closing in on a return from a cruciate knee ligament injury and could be available in time for his side's clash with Chelsea at Stamford Bridge on 5 November.
Mourinho was also unable to offer any good news on the injured midfield trio of Paul Pogba, Marouane Fellaini and Michael Carrick, with Zlatan Ibrhaimovic still on the road to recovery with December a likely return date for the veteran Swede.