With Redknapp's Tottenham side looking like qualifying for the Champions League, his name has been strongly linked to the job of England manager almost since the moment Fabio Capello resigned in early February.
Schmeichel, however, said he felt Redknapp had more to achieve at the North London club.
"If I was him, having done all that at Tottenham, I would ask myself - 'why would I leave this? This hasn't even peaked yet,'" Schmeichel told Reuters at a media event at the Carlsberg brewery in Copenhagen ahead of Euro 2012.
"Harry is a great manager, he's proved that on many occasions, small clubs with no money, he's got them to perform at the highest level.
"He's now got a little bit of money and what he's done with Spurs is amazing, but if they [England] want an Englishman, what are the options?"
"Not only are you dealing with the players, whose mentality has changed enormously over the last five years, but also dealing with the press," he added.
"I don't think you get a fair deal."
"Absolutely not! I got asked yesterday if I have coaching or manager ambitions, and I don't.
"I don't think it's worth it. Obviously the guys that are in those jobs now believe it is, but I don't think it's worth the hassle. And it is hassle."
"I went through all the fixtures this morning, and I challenge anyone to do the same and come up with a different result," he said.
"They are the strongest two teams in the competition."
"The only truth in that is that we had switched off," he said. "We'd finished our seasons for our clubs, the Danish season was actually still going on, but the players that played abroad had switched off.
"We were reporting for training every day but it was very casual. Then there was one day when we had two training sessions, we were in the middle of lunch when the word came that we were in.
"But it's a great story and I'm sorry to have killed it!"
