The Albania international spent last season on-loan with Everton, though his time on Merseyside was marred by injury.
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Burnley are aiming to sign Broja outright, with a five-year contract already tabled to the player's camp.
BBC Sport says the Clarets aim to do business for around £20m and aim to close an agreement early next week.
For his part, Broja has already approved the move and is now waiting for the two clubs to reach terms.
