Sky Sports understands Appleton - who has only been in charge at Blackpool since November - wants to leave the club.
He will meet with Blackpool chairman Karl Oyston on Thursday afternoon.
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.
Appleton has won two and drawn seven of his 11 Championship games in charge of Blackpool, who lie 14th in the standings - six points shy of the play-offs - and are one point and one place behind Blackburn.
Rovers caretakers Gary Bowyer and Terry McPhillips - who have overseen three wins out of three in their interim spell - will be in charge against Wolves on Friday night.
"It's a board matter," said Bowyer. "I think it would be wrong of me to comment on a manager at another football club.
"Until we're told otherwise we'll continue to do what we've done and that's prepare the players for Friday's game.
"I was notified last night and told that the official approach had been made, like I have been with everything that's gone on in our time here."