Churlinov has been a man in demand this summer, with Stuttgart prepared to let him move on for the right price.
He is now closing in on joining Burnley and was left out of Stuttgart’s squad for their meeting with Werder Bremen on Saturday to undergo a medical with the Clarets.
According to German daily the Stuttgarter Nachrichten, Burnley will pay an initial €3.25m to Stuttgart to sign Churlinov.
The total fee will eventually come up to the €5m mark when further bonuses and add-ons are paid.
Churlinov spent last term on loan at Schalke in the German second tier and impressed, leading to several clubs being keen on him this summer.
Vincent Kompany’s former club Anderlecht wanted to land Churlinov.
However, the 22-year-old winger was clear that he wants to join Burnley and rejected an approach from Anderlecht.
Stuttgart sporting director Sven Mislintat said on the matter of Churlinov’s move: “Very confidential talks have taken place and the matter is well advanced.”
Burnley next face Hull City in the Championship on Tuesday night.