Shearer is still a legend with Rovers fans and would be a very popular choice as the next manager and the man himself has said that he would be interested in holding talks with Rovers over the vacancy.
The 42-year-old football pundit had a brief time in the manager's chair at Newcastle, but gaining only five points from eight games, he was unable to save them from relegation.
Shaw told Sky Sports: "I'm sure it would (be a popular appointment), but even more than getting fans excited we need a good manager who'll get us to the Premier League and keep us in the Premier League.
"Obviously someone with Alan's football record, he'll be on the list that we have a good look at.
"I wouldn't confirm anything at this moment in time. There's a number of names being put forward for our job, those names have been forwarded on to the owners with comments.
"We're possibly getting a little bit nearer the interviewing stage but there's no one ruled in and no one ruled out at the moment, so I can't really comment any further."