The Senegal international held secret talks with the club during a recent trip to Istanbul, according to The Express.
However, Arsenal and West Ham United are both said to be interested in taking Ba on loan, as are Beskitas's Turkish rivals Galatasaray and Fenerbahce.
A Turkish club is thought to be Ba's preferred destination, while Chelsea are said to be reluctant to loan the player out to a domestic competitor.
"I talk closely with Demba Ba, he wants to play for a Turkish club but I can't comment on a transfer yet," said FIFA agent Ceylan Caliskan.
Ba has made 16 appearances for Chelsea since joining the club from Newcastle United last season, scoring two goals.