The national team has been without a coach since Fabio Capello left by mutual consent in February.
Shearer has said that it is crucial to England's Euro 2012 preparations for the new system to be in place sooner rather than later.
"They need a manager pretty soon - actually now," the 41-year-old told BBC Sport. "The FA should think about England rather than the other football clubs.
"The FA are in a very difficult position because if they go in with an approach then it would upset people. But now the time has come and so be it if they upset one or two people."
"Just because Harry has had a couple of bad results, it doesn't make him a bad manager. I would absolutely 100% still go for Harry Redknapp and I think everyone will tell you the same story."
England's next game is a Euro 2012 warm-up match against Norway in Oslo on May 26.