Jones and Rojo have both been on the sidelines for the Red Devils in recent weeks, with neither centre-back representing their club since the start of February.
Rojo turned out for Argentina during the recent international break, however, and Mourinho has said that both players are fit for the Swansea match, with Daley Blind the club's only outfield injury at this moment in time.
"Apart of Daley, who is training with us, but obviously not available after a couple of months out, we recovered all the other problems we had. That includes Phil Jones, of course Marcos Rojo, who played already with Argentina, so the picture improved a lot for us in that aspect," he told reporters.
"[Sergio] Romero is injured and I think he will be for a few weeks. I think in general he was lucky because it was a strong contact, a strong contusion, and he will take a little bit of time to recover. Ashley Young had a problem in the last part of the game against Italy, but we think there is a chance for him to recover."
United are currently second in the Premier League table, but would drop to third ahead of kickoff if Liverpool overcome Crystal Palace in Saturday's early start.