The Championship outfit are in the hunt for a new boss following the resignation of Steve Kean last month and former Newcastle United coach Shearer has been a name linked to the position.
"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," Shaw told The Guardian.
"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 been a lot of people inquiring about the job. Some people [who are] in work, some people out of work. I would have thought [there has been] about 20 good, proper applications."
Meanwhile, Shearer has revealed that he would consider taking on the Blackburn job.