Rovers have been without a manager since calling time on Henning Berg's 10-match reign two days after Christmas.
And a search headed by the club's global advisor Shebby Singh has settled on Lancashire neighbours Blackpool, who appointed Appleton just two months ago.
Blackburn's managing director Derek Shaw told the club website: "I can confirm that we have made an official approach to Blackpool FC about our interest in speaking to Michael Appleton.
"This is the only candidate we have approached for the manager's job."
Blackpool issued a statement confirming Blackburn "made a formal approach to speak to Michael Appleton", but added: "The club will be making no further comment at this stage".
Appleton left Portsmouth for Bloomfield Road in November following Ian Holloway's departure and has lost just two of his 12 games in charge.
Reserve-team manager Gary Bowyer has been in temporary control at Blackburn, meanwhile, winning all three games.