The Hammers are joined by Italian giants AC Milan, Inter, Roma and Napoli as well as Arsenal who have shown an interest in the 26-year-old previously.
Jordan, a Spanish central midfielder, has been a mainstay in Julen Lopetegui side this season, making a staggering 40 appearances across all competitions.
Operating as both a box to box player and a defensive midfielder, Jordan has contributed two goals and seven assists so far this term.
Although no fee is mentioned in the report, the Spaniard holds a market value of around £21.5m (Transfermarkt).
Therefore, midfield options are a necessity, especially if the Irons are competing on a European front.