The pair spoke candidly following England's 3-2 friendly win at St James' Park on Sunday night, when they settled the score against old Italia 90 rivals Germany.
Shearer also broke his silence on the matter, saying that everyone - including himself - was 'in limbo' over the failure to appoint a new manager at Newcastle.
The club has just days to make a decision before the start of the new season.
Gazza said: "It's unbelievable that people in the club don't know what's happening.
"They should appoint Alan Shearer as manager now and get it sorted out.
"It's a matter of giving Alan the job right now."
Lee added: "I have said all along that he (Alan Shearer] should be the manager at this club."
Asked about what he knew, Shearer said: "I want it sorted out as quickly as anyone else does. I'm a fan, just like anyone else.
"I don't like to see the situation the club is in."
He added: "I know as much as you do.
"I'd dearly love it to be sorted out one way or the other - the club needs to move forward.
"I'm the same as anyone else - I'm in limbo."
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