The 26-year-old midfielder was watched earlier this week as the Hammers look to continue strengthening their squad, despite already spending close to £100m on new acquisitions this summer.
French publication L'Equipe report that Manuel Pellegrini's side could find themselves in prime position to snap him up, though they will face stiff competition from Lazio and Wolfsburg for a player valued around the £15m mark.
The Hammers will need to act quickly if they want to get their man though, with both aforementioned clubs believed to have already submitted offers for the defensive midfielder.
Should he make the move to the London Stadium, Mendes would provide stiff competition for new signing Jack Wilshere, as well as more established Hammers stars such as Mark Noble, Cheikhou Kouyate and Pedro Obiang.
Mendes has spent the majority of his career playing in his native Brazil, representing Goias and Sao Paulo before moving to Ligue 1 with Lille last year. He has been in and out of the side since his arrival though, scoring three times in 17 appearances.
Any deal is likely to signal the end of West Ham's transfer business this summer, with the club having spent a record fee of around €40m to sign Lazio star Felipe Anderson last week.
Instead, new manager Manuel Pellegrini and director of football Mario Husillos are likely to turn their attentions to keeping hold of star asset Marko Arnautovic, who continues to be linked with a move away from the club after an impressive second half to last season.