Sabitzer followed Julian Nagelsmann to Bayern Munich last summer but he has found little joy in Bavaria and has been a bit-part player.
The Austrian is thought to be unhappy that the man who made him captain of RB Leipzig is not giving him the same opportunities at Bayern Munich.
He is keen to move on in the summer and Bayern Munich are also open to offers for him at the end of the season.
Arsenal are amongst the clubs who have an interest in Sabitzer, but according to Turkish daily Takvim, Fenerbahce are now also in the race.
It has been claimed that ROGON Management, the agency representing Sabitzer, have offered him to Fenerbahce.
A proposal is in front of the Fenerbahce hierarchy, who are drawing up plans for the summer transfer window.
The Turkish giants are considering signing him with a view to adding a top-class midfielder to their squad.
Fenerbahce are plotting to sign him on an initial loan deal in the summer with a mandatory purchase clause, but it remains to be seen if those terms would suit Bayern Munich.
