Fenerbahce have held talks with both Mehmet Topal and Gokhan Gonül whose contracts expire at the end of the season.
The duo have been subject to interest from abroad however, both are keen to remain at the Istanbul giants.
Fenerbahce president Aziz Yildirim insisted that talks be held without the players agent present.
The Milliyet newspaper states that Fenerbahce will offer €1.75 million per-season to both players.
Topal’s agent Batur Altiparmak is however, remaining coy over the latest transfer rumour and refused to rule out the possibility that he may leave.
Altiparmak told Turkish-football.com: “Everybody writes something different every other day so I am not going to respond to every transfer rumour.
“Let us wait until the end of the season and see what happens.”
Topal has two goals and three assists in 45 appearances for the Yellow Canaries this season.