The English publication suggests that an announcement for the pair could come within the next 24 hours, as Manuel Pellegrini appears to have acquired two targets he's been chasing throughout the transfer window.
A £7m deal has reportedly been agreed with the Swans for Fabianski, although the club are waiting to confirm the transfer due to his involvement with Poland at the World Cup, and will announce his signing until after their opening game against Senegal.
Diop meanwhile recently underwent a medical at the Premier League side ahead of a proposed £21.9m move, and should he complete his expected move to the London Stadium, comes with a glowing reputation following his time in Ligue 1, captaining Toulouse despite being only 21 years old.
Fabianski and Diop would join Ryan Fredricks at West Ham, after the right back joined the Hammers following the completion of his contract at Fulham, as Pellegrini looks to fix a defence that conceded the joint-most goals in the division last season with 68.
Another name linked with a move to West Ham is Fabianski's teammate Alfie Mawson, with the centre back remaining a target for a number of clubs alongside Pellegrini's side following Swansea's relegation from the Premier League last season.
One deal however that appears to be on hold is is the signing of Lazio winger Felipe Anderson. The Italian side appear to want £35m to part ways with the Brazilian, while West Ham value the 25-year-old at around £25m.