The top job at Wembley has been left open ever since the Italian resigned in February, with the governing body yet to make an announcement about a replacement.
Tottenham manager Harry Redknapp remains the overwhelming favourite despite a bad run of form domestically, but it remains to be seen if it will be him or someone else who leads the Three Lions into this summer's European Championships.
Premier League managers have been told to avoid commenting on the job in the media so as not to disrupt other clubs, but Shearer wants a quick end to the uncertainty.
"The FA are in a very difficult position because if they were to go in and (make an) approach, it would upset people," the 30-goal international told BBC Sport.
"But I think the time has come, because England need a manager in now to prepare, to look at things and maybe organise things.
"Maybe the FA should think about England rather than other football clubs, but they're in a tough position."
Tottenham's descent from title challengers to scrapping for Champions League qualification has left some asking whether or not Redknapp should still be considered.
As a result, names such as Roy Hodgson and Alan Pardew have been mentioned, but Shearer still thinks Redknapp is the man.
He added: "Just because Harry Redknapp's had a couple of bad results, doesn't make him a bad manager,
"I'd still absolutely, 100%, go with Harry and I'm sure everyone would tell you the same story."