The 24-year-old has established himself as one of the best players in the Eredivisie, ending the most recent campaign as top scorer in the division with 21 goals.
That return has resulted in interest in the Iran international's signature, and his agent has previously revealed that talks are ongoing with an unnamed club.
According to The Mirror, Brighton and Leicester are showing an interest in completing a £20m deal for the player before the start of the new Premier League campaign.
Seagulls boss Chris Hughton has already made six first-team signings, but it has been suggested that Brighton are still willing to break their transfer record to bring in Jahanbakhsh.
Leicester have money to spend after the sale of Riyad Mahrez to Manchester City, with the Foxes yet to find a replacement for the Algerian playmaker.