Moyes has found things hard going since taking over from Sir Alex Ferguson at the start of this season, leading United to seventh in the Premier League table while also being eliminated from both domestic cup competitions.
Their participation in the Champions League could also end tomorrow night when they face Olympiacos with a two-goal deficit in the second leg of their last-16 tie, and Michel made it clear that he would not be doing his opposite number any favours despite his support for Moyes.
"David Moyes is suffering and I don't like to see any manager suffering. I have sympathy for him," Michel told reporters.
"We know he works hard, but sometimes results don't mirror the hard work done. It's nothing personal to David Moyes. It's a big opportunity to knock Manchester United out of the competition, but David Moyes is not an enemy."
United's last outing saw them comprehensively beaten 3-0 at home to bitter rivals Liverpool.