The Sweden international is itching for a move this January after making just one appearance all season.
Hamburg are willing to rubber stamp a deal if the price is right and a number of clubs have since expressed an interest.
Indeed two sides at the front of the queue, according to Swedish newspaper Aftonbladet, are Burnley and Sunderland.
The Premier League duo are reportedly both keen on Bahoui and they are ready to scrap it out for his signature during this month's transfer window.
However, as well as Burnley and Sunderland, Greek side AEK Athens and Spanish club Las Palmas are also interested in striking a deal.