The Senegal international has been part of the set-up at Stamford Bridge since completing a switch from Newcastle United in January 2013.
He has scored a number of important goals during his 18 months in west London, but has found regular starts hard to come by.
That situation is unlikely to improve on the back of Diego Costa’s big-money arrival from Atletico Madrid - and with further attacking additions being mooted.
With Ba expected to be on the move this summer, interest in his services has been building steadily.
Turkish clubs have led the chase in the past and are back in the hunt as they look to lure the former West Ham United frontman away from the Premier League.
Besiktas claim they are close to agreeing a deal, with Chelsea prepared to compromise when it comes to the setting of a fee.
Club president Fikret Orman told NTV Spor: "Demba Ba is an excellent player, we have been in talks with Chelsea for a long time over bringing him to Istanbul.
"Talks are ongoing. Chelsea initially wanted £10million for Ba but we have negotiated a price we are happy with.
“We'll tell the media once the final deal is done."