It is reported by Gazzetta TV, as relayed by Tutto Mercato Web, that the Toffees are keen on the Frenchman, who has become a regular and consistent member of the Udinese team in Serie A.
This summer there are likely to be plenty of players linked with heading to Watford from Udinese, who are also owned by the Pozzo family. It was reported by the Watford Observer last month that Heurtaux was one such player.
The 26-year-old centre-back has been a regular in Serie A in and is one of the most consistent performers in the Italian league.
However no such deal has materialised and now Everton might swoop.
Do the Toffees need him?
The club were short at centre-back last term and the likes of Antolin Alcaraz and Sylvain Distin, who did not impress in 2014-15, have both departed the club.
Add to that the report on the back of The Mirror this morning that star youngster John Stones is set to be the subject of a bid from Chelsea that will exceed the £31.9 million British record for a defender.
Everton need a central defender with more star quality than Heurtaux but his arrival would be an astute and assured piece of business from Roberto Martinez, if he can pull it off.