According to Goncalo Lopes, who is a very reliable journalist covering Portuguese football, the Toffees have submitted a bid in the region of £13.4m (€15m) for the midfielder.
Earlier this month, Esporte News Mundo claimed that Everton boss Carlo Ancelotti had personally phoned the player.
The Toffees are looking to bolster their defensive midfield options in the next transfer window and have earmarked Wendel as a potential option.
The likes of Morgan Schneiderlin is expected to leave the club, and Wendel would be a superb addition to the side.
Sporting are looking to sell some of their players in order to balance their books ahead of the new season.