After experiencing relegation with the Clarets, the striker has made it clear that he does not want to spend next season in the Championship.
The January signing has become of interest to Turkish sides Fenerbahce and Besiktas, who are in the market for a man up front.
Burnley are claimed to be open to letting him leave on loan in the summer but his destination may not be Turkey.
Europa League winners Eintracht Frankfurt have entered the fray for the striker, according to German daily Bild.
The Clarets signed Weghorst from Eintracht Frankfurt’s fellow Bundelsliga club Wolfsburg, where he also worked with the current coach of the Europa League winners, Oliver Glasner.
Eintracht Frankfurt have qualified directly to the group stage of the Champions League next season, while Fenerbahce have to go through the qualifiers and Besiktas do not have any European football to offer.
Weghorst scored only two goals in 20 appearances for the Clarets and wherever he ends up next season, he will be hoping his form picks up and he gets on the scoresheet more often.