The Turkish daily newspaper claims that Fenerbahce have reached an agreement with Lille and the Danish international and that Kjaer will be in Turkey at 13:30 (GMT) tomorrow.
Liverpool have expressed an interest in Kjaer according to L’Équipe. Lille are understood to have slapped a €10 million price tag on the Danish international.
Fenerbahce are looking to build a strong squad in preparation for next seasons UEFA Champions League campaign.
The clubs new Director of Football Giuliano Terrano has requested two defenders and a midfielder before the club searches for a new striker.
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.