The Turkish newspaper Milliyet have claimed that the Eagles have been in contract with United and want to bring the Mexico international in on a permanent deal.
The report goes onto state that Besiktas have set aside €6million for the 27-year-old.
Besiktas are on the hunt for a new striker after selling last seasons top scorer Demba Ba to the Chinese club Shanghai Shenhua for €13 million last week.
Hernandez spent last season on loan at La Liga giants Real Madrid after falling out of favour with Manchester United boss Louis van Gaal.
The former Chivas striker’s future is unclear following a broken collarbone which will rule him out of the Gold Cup. The injury is expected to keep the Hernandez out of pre-season training for another three weeks.