The former Liverpool skipper took over at the German outfit last term and finds himself making his Champions League debut opposite Moyes at Old Trafford tonight.
He is trying to increase the pressure on Moyes, who has not enjoyed the smoothest of starts.
But even if Leverkusen extend an amazing recent run of four home defeats in six European games at Old Trafford for the Red Devils, Hyypia is sure the Scot will eventually get it right.
"David Moyes is an experienced manager," said Hyypia. "Everyone should give him more time to get things running.
"Hopefully it doesn't happen against us. We have to stop them getting their rhythm and make sure they don't score in open play.
"Then we need to be very aware at set pieces."
Hyypia has already endured one of the best and worst days of his career at Old Trafford, that came six years apart.
"I was sent off after four minutes and watched the rest of the game in the dressing room," he said, of his 2003 experience. It was the only red card of my career and we lost 4-0.
"You remember those kinds of things but the first one that comes to my mind is playing my last game here, when we managed to win 4-1.
"I only knew I was playing two minutes before kick-off and it was my last 90 minutes for Liverpool."
Signed by Gerard Houllier in 1999, it did not take Hyypia long to realise the rivalry that existed between Liverpool and United, even if he would prefer to distance himself from it now.
"Coming from Finland, I knew something about the English game and that Liverpool and United were rivals," he said.
"I didn't realise it was quite as fierce as it was though. People started speaking about the United games weeks before they were actually played.
"That kind of stuff means more to the fans though. To us it was just another game, and now I am with Leverkusen, not Liverpool."
Leverkusen have started the German season well, posting four wins from their opening five games.
Jens Hegeler and Gonzalo Castro have both been ruled out through injury but Hyypia expects to have star man Lars Bender and last season's Bundesliga top scorer Stefan Kiessling available.