Appleton, who was only appointed as Blackpool boss on November 7 following Ian Holloway's departure to Crystal Palace, emerged on Tuesday as the surprise bookmakers' favourite to succeed Henning Berg at Rovers.
And Blackburn on Wednesday evening confirmed they have been in touch with their npower Championship counterparts in the hope of talking to the 36-year-old.
A statement on Rovers' official website, www.rovers.co.uk, attributed to managing director Derek Shaw, read: "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 managers' job".
Appleton has won two and drawn two of 12 games since taking the reins at Bloomfield Road. His most recent victory was a 2-0 home triumph over Blackburn on December 15.
That result was Rovers' fourth defeat in five matches and a 2-0 reverse in their next outing at Middlesbrough cost Berg his job after 10 games at the helm.
Last week Blackburn issued a statement to confirm reserve team manager Gary Bowyer would remain in charge of first-team affairs until the end of January alongside head of youth Terry McPhillips, following consecutive league wins in the immediate aftermath of Berg's sacking.
FA Cup victory over Bristol City duly followed last weekend, although the approach for Appleton means it appears unclear whether Bowyer and McPhillips will see out the month.
Blackburn currently lie 13th in the Championship, one point and one place above Blackpool, who travel to Charlton on Saturday a day after Rovers take on Wolves at Molineux.
Blackpool issued a brief statement in response which read: "Blackpool FC can confirm that on Wednesday evening Blackburn Rovers FC did make a formal approach to speak to Michael Appleton.
"The club will be making no further comment at this stage."