Moyes' critics came out in force three weeks ago when his United team lost 2-0 to Olympiakos in the first leg of their Champions League last-16 tie.
The pressure on the Scot will no doubt intensify if his team put on another poor showing in the return leg, especially as the match comes three days after a dismal home defeat to Liverpool.
But the man who will be in the opposing dugout at Old Trafford, Michel, appears something of a reluctant potential assassin.
"David Moyes is suffering and I don't like to see any manager suffering. I have sympathy for him," the Olympiakos manager said.
"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."
Alejandro Dominguez and Arsenal loanee Joel Campbell scored against United in Athens, where the away side struggled to create any meaningful chances until Robin van Persie missed a good chance at the death.
Michel's team lost their unbeaten record in a derby against Panathinaikos soon after the United win and they lost again to PAOK Salonika the week after.
However, the Greeks bounced back with a 2-0 win over Panthrakikos on Saturday to clinch their 41st league title with five matches to spare.
Less than 24 hours later Michel was at Old Trafford to watch United lose 3-0 to bitter rivals Liverpool.
The former Real Madrid midfielder was impressed by the noise generated by the capacity crowd, but Michel is sure his players will not wilt under the pressure of playing in front of 75,000-plus fans.
"My players aren't scared of anything," said Michel, who guided Olympiakos through a group containing Paris Saint-Germain, Anderlecht and Benfica.
"Maybe I am a bit more scared than them, but as they're playing, I can assure you they won't be scared of anything.
"We've played big clubs in big grounds."
Part of the reason behind Olympiakos' success at home and in Europe this season has been the form of evergreen striker Javier Saviola.
The 32-year-old has missed the club's last four matches with a thigh injury, but he has travelled to Manchester with the rest of the squad.
Michel would not reveal whether the club's top scorer would feature, though.
"Javier Saviola is doing fine, thank you very much," was all the Spaniard would say when quizzed about the Argentinian's fitness.