The 26 year old midfielder is reported to be on the verge of returning to the Super Lig with Aykut Kocaman's side reaching an agreement with Los Che.
The 26 year old, who joined Los Che from Fenerbahce's fierce rivals Galatasaray in 2010 in a deal worth €5.5 million has featured 30 times for Unai Emery's side this season, scoring twice.
According to the report, the deal is due to be announced after Turkey conclude their international games in May, with Topal a member of the squad due to play against Portugal and Ukraine.
Fenerbahce president Aziz Yildirim was rumoured to be in the market for a midfielder, and the acquisition of Topal is reported to be in the region of €8 million.
Furthermore, the Turkish giants have also been linked with Valencia midfielder Tino Costa, with the deal bringing both to Sukru Saracoglu thought to cost around €14 million.
The Yellow Canaries ended the Super Lig season in second place, qualifying for the Champions League.