United are into the Europa League semi-finals after Marcus Rashford sealed victory over Anderlecht in extra-time of a match which saw both Marcos Rojo and top scorer Ibrahimovic forced off with injuries.
But the win came at a cost as increasingly important defender Rojo left the field on a stretcher in the first half, before Ibrahimovic's knee buckled after landing awkwardly just before extra-time.
Asked about the condition of the pair after the match Mourinho said: "I want to wait, but my feeling is not good for both. I want to wait and try to be optimistic, but I am not."
But Shaw appears to be more positive than his manager telling reporters the Swede was already moving better.
"He's fine. He was walking around in the changing room," Shaw said when quizzed on his teammate's health.
Rojo's injury leaves United without three first-choice centre backs with Mourinho calling on injured pair Phil Jones and Chris Smalling to be "brave" and help the team's cause.
"We have Daley Blind, who has experience in the position, and I think it is time for Jones and Smalling to be brave - to risk," he said. "Because for the team you have to do everything, that is the way I think.
"You cannot do miracles, so miracles I don't expect, but they have to try to do everything to accelerate the process.
"They have injuries, and even with a crazy mentality, they cannot play Sunday (at Burnley in the Premier League).
"But with a special spirit, you can (come back) sooner than expected. So instead of mid-May, it could be the beginning of May, this kind of acceleration of the process."