Both Liverpool and West ham have both been monitoring the Lille defender since the start of the year but look like they will miss out on the 26-year-old.
Kjear is currently in Istanbul holding talks with Fenerbahce and is close to putting pen to paper on a three-year deal according to the Hurriyet.
Southampton have also been linked with the former Wolfsburg centre-back as a replacement for Toby Alderweireld.
The Istanbul giants are planning to strengthen their squad ahead of next seasons UEFA Champions League play-off round.
Fenerbahçe recently appointed Giuliano Terrano as the clubs director of football and Vitor Pereira as manager on a two-year deal last week.
Fenerbahçe finished the league season as runners up and booked a place in the Champions League play-off stages.
The Yellow Canaries will participate in European competition for the first time in two years after serving their UEFA suspension.