Shearer, Rovers' top scorer when they won the Premier League in 1995, told BBC Football Focus on Saturday he would speak to the club if approached to succeed Steve Kean.
In his only previous managerial spell, Shearer took five points from eight games in a failed attempt to save hometown club Newcastle from relegation three years ago.
Reports on ESPN Soccernet on Sunday quoted an unnamed Blackburn source as claiming owners Venky's "would like to assess the possibilities of Alan Shearer taking the job" following three Championship games without a win under caretaker manager Eric Black.
Former Preston chairman Shaw suggested the recruitment process is not at such an advanced stage and, although paying tribute to Shearer's standing within the game, he insisted the 42-year-old's popularity among a fanbase disgruntled by Kean's troubled tenure should not be a decisive factor in any decision.
He said: "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."
Former Manchester United duo Roy Keane and Ole Gunnar Solskjaer are among a host of names to have been linked with the Ewood post over the past week along with ex-Real Madrid boss Bernd Schuster.
Shaw would not be drawn on specific names but confirmed Blackburn are in the healthy position of selecting from a strong list of candidates.
He added: "There's been a lot of people enquiring about the job - some people in work, some people out of work.
"I would have thought (there has been) about 20 good, proper applications."