Szalai made 43 appearances in all competitions for the Istanbul giants in the 2021/22 season, scoring once and assisting on two occasions.
The defender, who has also played at left-back for Fenerbahce, was a vital player as Hungary beat England twice in the recent round of UEFA Nations League fixtures.
Fenerbahce are tipped to sell the Hungary international if offered the right price this summer and, according to Turkish outlet En Son Haber, Newcastle are keen.
Szalai is viewed by the Magpies as an alternative to Botman, whose future remains uncertain due to reigning Serie A champions AC Milan’s financial situation and Lille’s demands.
Newcastle are likely to face competition from Napoli, who are also interested in signing the Hungarian international as a replacement for Kalidou Koulibaly.
Eddie Howe wants a defender and his first choice is Botman, but Newcastle are prepared to switch to alternatives if no deal is done soon.
And the jury is out on whether they will switch their attention to Hungary international Szalai.