Shearer, 38, scored 206 goals in 404 appearances during a 10-year playing stint to earn legendary status on Tyneside.
And the former England striker, who retired from playing in 2006, has made no secret of his desire to become a manager one day.
So far though he has played down talk of venturing into management with his former club.
Newcastle, who are up for sale, are currently managed by Joe Kinnear - who was handed an interim role at St James' Park by owner Mike Ashley after Kevin Keegan quit the club in September over his lack of control on transfers.
Shearer, now a pundit on BBC TV's Match of the Day, is believed to be put off from returning to St James' Park by the structure at the club.
In the present set-up, executive director Dennis Wise has a significant role in the identification and purchase of new players.
Shearer told BBC Sport in September he would not be the next Magpies boss
"I'd like to be a manager at some point in my career," Shearer told BBC Sport's Football Focus in September.
"But I want to manage - and control who comes in and out of the club."
Lee feels Ashley would do well to approach Shearer and tempt him back to the club as manager, but also recognises that the structure of the club would have to change.
"The fans would love Alan to take over now," said Lee, who made 303 league appearances for Newcastle between 1992 and 2002.
"Mike Ashley would solve a lot of his problems by appointing Alan and accepting that mistakes have been made. Alan could be a priceless 'get out of jail' card.
"Now is the time to make the club what we all want."
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