The 31-year-old is currently enjoying a temporary stint at Hoffenheim in the German first division, having not played for the Clarets for over a year.
Weghorst has fared steadily in the Bundesliga so far this season, scoring five times and assisting once in 22 appearances for Pellegrino Matarazzo's men.
Since his last match for the Lancashire club, the Dutchman has played on loan at Hoffenheim, Besiktas and most notably Erik ten Hag's Manchester United.
Since securing a permanent switch from Bundesliga side Wolfsburg to Turf Moor in January 2022, the striker has netted just twice in 20 appearances.
Burnley man wanted in Turkey?
According to Fanatik, Turkish Super Lig side Trabzonspor are looking to bolster their attacking line ahead of the 2024-25 campaign under Abdullah Avci.
The report claims that the Trabzon-based club are interested in securing the services of Burnley man Weghorst, whose future looks set to be away from Turf Moor.
It is understood that Trabzonspor wanted to sign Paul Onuachu permanently this summer following his temporary spell from Championship side Southampton.
However, Russell Martin's Saints are said to be demanding £8.5m for the Nigerian - a price tag that the Turkish club have deemed too expensive.
Therefore, Avci's men have swiftly moved onto other attacking targets, with one of those being the Burnley marksman, who has been left in the wilderness at Turf Moor.
Trabzonspor face competition for Weghorst
It was reported earlier this month that Eredivisie side FC Twente are keen on securing the signature of Weghorst, who has a special connection to the Dutch club.
The 31-year-old supported the Tukkers as a child and has openly expressed of his desire to play for Twente before he retires from professional football.
It has been suggested that Weghorst is willing to take a significant pay cut in order to link up with the Tukkers for the 2024-25 campaign.
With just over one year left on the Dutchman's contract at Burnley, it is believed that the Clarets are looking to offload the forward at the conclusion of the term.