The Toffees and their Premier League rivals from White Hart Lane are among a host of clubs said to be weighing up the merits of a move for a highly-rated 19-year-old frontman.
Top sides in France are also ready to pounce, with Nangis having impressed since bursting onto the senior stage.
He claims to be happy where he is, and is looking forward to gracing the European U19 Championship with France this summer.
Nangis is, however, prepared to admit that interest in his services is mounting steadily.
He said: "I am very happy with my form so far and I am looking forward to the U19 tournament in Lithuania.
"There are English clubs interested and also top French clubs, but I am very happy at Caen at the moment.
"Everton and Tottenham are top teams who make your head turn, but I need to focus on the upcoming championship."