Rooney picked up a “deep” muscle injury prior to Man United’s Boxing Day win over Sunderland.
Shaw, who limped off during United’s 4-1 League Cup win over West Ham United, has been out for over a month with a calf problem.
Speaking ahead of Saturday’s game with Middlesbrough, Mourinho made it clear that the pair would not feature against Aitor Karaoke’s men.
“No, but he’s not ready [for the Middlesbrough match],” he said.
“Luke is training now with the team without any problem, but I don’t think he is ready to start the game [either].”
Rooney’s absence could pave the way for Juan Mata and Henrikh Mkhitaryan to feature in the same starting XI. Such creative zeal on each flank would open up plenty of space for Zlatan Ibrahimovic – who has 11 goals in his last ten games – to exploit as he looks to cement himself as 2016’s top goalscorer with two more goals.
Shaw’s absence, on the other hand, will provide Daley Blind – an assured force at left-back on Boxing Day – with another chance to assert himself on Mourinho’s starting XI.