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?"
Having played in England for Manchester United, Manchester City and Aston Villa, the former goalkeeper is also well aware of the difficulties faced by the England manager.
"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."
Schmeichel laughed off suggestions that he might throw his own hat into the ring for the job.
"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."
Still revered in his home country for his part in the Danish side that won the European Championships in 1992, Schmeichel has predicted either Holland or Germany would win the Euro 2012 tournament.
"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."
Schmeichel, who also acts as a global ambassador for the Danish brewing giant that is a sponsor of the Euro 2012 tournament, said he was also keen to put an end to the myth that many of the 1992 Danish side were on holiday when they received the news they would replace Yugoslavia at the tournament.
"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!"
