According to the Mirror, West Ham have already agreed a deal for Diop with French side Toulouse, as Manuel Pellegrini looks to strengthen his Hammers defence ahead of the upcoming season.
However, it would seem Pellegrini now faces competition for the 21-year-old from Everton, who also have a new manager looking to bring in his own recruits in the form of Portuguese boss Marco Silva.
The report claims that a host of European clubs are interested in the defender, including Marseille, Monaco and RB Leipzig. Any one of these clubs may be more appealing to Diop due to the promise of European football in the 2018/19 season - an incentive which neither West Ham nor Everton can offer the player.
Diop made his debut for Toulouse in November 2015 as an 18-year-old, having come through the French outfit's youth setup. He has gone on to make 85 appearances for the club, scoring five goals in the process. Diop has also represented France at every youth level from Under-16 through to Under-21.
Both Everton and West Ham are looking to improve following disappointing campaigns in 2017/18. Everton spent nearly £150m last summer in their attempts to challenge the top four but ultimately finished in eighth place, sacking manager Ronald Koeman in October and replacing him with Sam Allardyce.
West Ham, meanwhile, sacked Slaven Bilic in November 2017 and spent much of the season fighting relegation. Though the club went on to finish 13th, the Hammers dispensed with the services of manager David Moyes just days after the end of the season - the same day that Everton sacked Allardyce.