Rooney was on the bench for Thursday's quarter-final as he recovers from an ankle issue and there has been intense speculation about the forward's future after he was left out of the England squad in March.
Dyche's side welcome Jose Mourinho's men to Turf Moor for a Premier League game on Sunday and the Burnley boss backed United's skipper and record goalscorer Rooney to compensate for Ibrahimovic's expected long-term absence.
"They're not short of options, without a shadow of a doubt," Dyche told reporters.
"The one everyone thinks is not that good anymore, I think he's decent - the boy Rooney, I always think he ain't bad. I certainly think if they chose to play him, I don't think he would let anyone down.
"You get to an age where you're questioned regardless of performances. He's a top-class player; you can't achieve what he's achieved in the game and not be a top-class player. You can't cheat the system. Whatever his journey forward is he will remain a top-class player in my eyes."
37 - Zlatan Ibrahimovic has been directly involved in 37 goals in all competitions this season; 22 more than any other Man Utd player. Blow.— OptaJoe (@OptaJoe) April 21, 2017
Burnley collected one of their meagre haul of four away Premier League points at Old Trafford in October - with former United goalkeeper Tom Heaton in inspired form during a 0-0 draw - and Dyche is expecting another tough day for his team.
"On that day I think they were the best side we've played this season," Dyche added. "We had to give every bit of air in our lungs to try and get something. Tom made saves and the defensive unit just stuck to the task.
"They're a fine side, in my opinion. There's a bit of noise about them being up and down but I still think they're a really good side with a top-class manager."