Shearer, who spent four years in the north-west between 1992 and 1996, scoring 112 goals in 138 appearances, was top scorer when Rovers won the Premier League in 1995 and is highly regarded by the club’s fans.
"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."
Speaking to the BBC's 'Football Focus' on Saturday, 42-year-old Shearer suggested he would speak to the club if they approached him, but according to Shaw his name is one of many on a lengthy list.
|BLACKBURN BOUCING BACK?
|9/1||Blackburn are 9/1 to win the 2012-13 Championship with bet365|
"There are a number of names being put forward for our job and those names have been forwarded on to the owners with comments," Shaw added.
"We're possibly getting a little bit nearer the interviewing stage but there's no one ruled in and no one ruled out.
"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."
Rovers fans will be hoping that a new manager is appointed soon following a disappointing run of three games without a victory in the Championship under caretaker manager Eric Black.