Jones, 25, spent most of the month of November on the sidelines, returning from the international break with a fresh injury problem that infuriated his manager. As a result, the England international sat out four Premier League matches before taking a spot on the substitutes' bench on Sunday against Manchester City.
Rojo, meanwhile, started his fourth game since returning from a serious knee injury against Pep Guardiola's side but was left with blood pouring from his head after clashing with David Silva in the first-half – picking up a yellow card for committing the foul in the first place.
The Argentina international left the pitch for treatment but returned to see out the first half wearing a thick bandage, before being replaced by Victor Lindelof for the second 45.
Ahead of the visit of Bournemouth on Wednesday, Mourinho suggested the former Sporting CP defender could be handed a rest, with Jones ready to step in. He told MUTV: "He is a brave guy. I don't know how he is – let's see if he can be ready for the match. But if he is not ready, we have other alternatives to play."
On the availability of Jones, he added: "Phil Jones was already on the bench at the weekend. The injury is behind him and hopefully he can stay fit for the rest."
Eric Bailly, meanwhile, remains unavailable, having also returned from the international break with a knock.
Defeat to City on Sunday leaves United 11 points adrift of runaway leaders City – who also brought a shuddering halt to United's undefeated run at home. Mourinho is now expecting a response from his side against the Cherries.
"When you lose you probably have a little bit more desire to win it," Mourinho said. "Nobody wants to lose once. Nobody wants to lose twice. Every team in the world, when you lose a match, the next one you have a little bit extra to give."