The Yellow Canaries are willing to offer €8m for the 28-year-old
Fenerbahçe have also been in talks with Benfica's Oscar Cardoza however, talks have recently stalled due to a disagreement over the Paraguayan internationals transfer fee.
Ba has been deemed surplus to requirements in Jose Mourinho's preferred squad make-up and has been transfer listed by Chelsea.
The Senegalese international striker joined the Blues last January on an €8.5 million move from Newcastle United scoring twice in 14 appearances for Chelsea.
The Canaries have strong ties with the board at Chelsea and brought in Raul Meireles on a €10 million move from the Premier League club last season.
Ba is a close friend of Fenerbahçe striker and fellow compatriote Moussa Sow however, the Canaries are facing increasing pressure over foreign player spaces.
The Turkish Football Federation (TFF) will only permit 10 foreign players per-club in the 2013-14 season and
allow six foreign players on the field at any one time.
Fenerbahçe currently have 11 non-Turkish players on their books.