Crystal Palace are also keen on the Senegalese international who was linked with Manchester United and Wolverhampton Wanderers earlier in the window.
PSG are looking to balance the books and are open to cashing in on Gueye who joined the French giants from Everton for £30 million last summer.
West Ham’s midfield was run ragged during their 2-0 loss to Newcastle United on Saturday, and they could do with a quality enforcer in the mould of the former Goodison Park star.
Hammers skipper Mark Noble is clearly approaching the twilight of his career and could do with an upgrade.
Gueye, 33, joined Everton from Aston Villa for around £7 million in 2016 and played 108 times for the Toffees before signing a four-year deal with the French champions.
He brings quality experience to the table and will be a quality short-term addition to the West Ham midfield.
No player in the Premier League attempted more tackles than Gueye in 2018-19, and he won 89 of the attempted 142, winning more tackles per game (2.7) than any player.
Gueye completed 75 interceptions in his last 33 top-flight league games, the sixth-highest in the Premier League, and the Hammers could do with such a quality player in the middle of the park.