The two sides face off at Old Trafford on Sunday afternoon, a little under 72 hours before the Red Devils take on Ajax in the final of the Europa League.
With little riding on the game, and zero knock-on effects at either end of the table, Mourinho believes that it could easily have been moved to Saturday afternoon and has threatened to field a number of youngsters.
Allardyce fully understands his opposite number's concerns over player fitness, but expects a tough match regardless of the side named by the hosts.
"Whether Jose plays a weakened side or not it'll be a difficult task. There's no doubt [the match could have been switched]," he told reporters.
"We moan about not getting near the Champions League, but there's no hope from the Premier League to give him the best chance. That wouldn't have happened abroad. Jose, tactically, with whatever team he picks is very, very good at setting it up."
Asked if he would have named a weakened side in similar circumstances, Allardyce added: "There's no doubt about that. It'd be wrong to risk anyone for that match."