The development represents a U-turn by the Seasiders, after initially rejecting Blackburn’s first approach earlier on Thursday.
However, Blackpool have now announced that both Appleton and first-team coach Ashley Westwood are set for talks with the Ewood Park outfit.
A statement on the club’s official website read: "Blackpool FC can confirm that following discussions with Blackburn Rovers and Michael Appleton, permission has been granted for the manager and Ashley Westwood to discuss personal terms with the club."
Appleton, who did not take training on Thursday and cancelled the weekly press conference due to the speculation, took charge of Blackpool on November 7 following Ian Holloway’s switch to Crystal Palace.
Managing director Derek Shaw confirmed in a statement that Appleton is the only candidate to have been formally approached: "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".
Blackburn’s global advisor Shebby Singh had hoped to make an appointment by New Year’s Day, with reserve-team manager Gary Bowyer currently in charge of first-team affairs.