The deal is believed to be valued in the range of €25 million (£22m), according to Sky Sports.
Diop is a France Under-23 international who played 37 times for his club last season.
The 21-year-old centre-back is seen as a huge prospect and West Ham want the deal wrapped up as soon as possible.
The club are also in talks to sign Lukasz Fabianski from Swansea.
There is a major push within the club to give new manager Manuel Pellegrini a squad capable of finishing in the European places next season.