The report states that Fenerbahce, along with bayer Leverkusen and Tottenham are in a race to sign the Mexico international.
Yellow Canaries are preparing to use part of the €16 million received from the sale of Moussa Sow to table a bid for a new striker.
Hernandez spent last season on loan at La Liga giants Real Madrid after falling out of favour with Manchester United boss Louis van Gaal.
Hernandez provided nine assists and scored nine goals in 33 appearances for Real Madrid last season.
The 27-year-old scored 40 goals in 74 international appearances for the Mexican national side.