The Belgian outfit put an article on their official website in the early hours of Monday morning – accompanied by a picture of Vossen with Brugge general manager Vincent Mannaert – which said they had “reached an agreement in principle” over the 26-year-old forward and he had penned a five-year deal.
Burnley, who only announced the signing of Vossen from Genk on July 6, have so far declined to comment on the matter.
Since moving to the Clarets on a three-year deal for an undisclosed fee, the Belgian has made five appearances in all competitions and is yet to score a goal for the club.
The first four run-outs were starts, but Vossen was then an unused substitute in the 1-0 Sky Bet Championship win over Brentford before coming off the bench in Saturday’s 2-1 victory at Bristol City.
He had previously spent his entire career on the books of Genk, scoring 105 goals in over 200 appearances for them.
Vossen had a loan spell at Cercle Brugge in 2009 and scored nine goals in 40 appearances for Middlesbrough during a season-long loan on Teesside from September 2014.