They face competition for his signature from Sevilla, who have made an offer, and the 'Hammers' are yet to reach an agreement on the fee for the player.
In addition, it is thought that the Frenchman wants better personal terms than are currently being offered, so it could be some time before any deal comes.
However, Diop is not the only player on the radar of the east London side.
Talks continued with Swansea over the signings of Lukasz Fabianski and Alfie Mawson, who could both leave south Wales after the 'Swans' relegation from the Premier League.
Talks have also restarted with PSG regarding Javier Pastore, but the player's wage demands are still a major sticking point.