Wolves are ready to pay around £5 million to acquire his services and the talks are progressing. The 33-year-old is keen on the move to the Midlands club.
Cresswell is with the Hammers on their pre-season tour of Australia but did not participate in their 3-2 comeback win against Tottenham Hotspur yesterday amid transfer speculation.
Wolves head coach Julen Lopetegui mostly used Toti Gomes and Jonny as his left-back options last season.
Rayan Ait-Nouri could barely get a look in, and they are now preparing for him to head out on loan.
They will need a replacement, and Cresswell, who joined West Ham from Ipswich Town, is their man.
The Liverpool-born defender has bagged ten goals and 37 assists in 331 appearances for the London club.
Cresswell graduated from the Tranmere Rovers youth system before debuting for the first team in 2008. He represented them for three years before joining Ipswich.
The former England international found game time hard to come by last season, with Emerson Palmieri firmly ahead of him in the pecking order.
However, he helped the Hammers win the Europa Conference League – their first European trophy since 1965.
Cresswell became famous for his corners and free kicks, earning a reputation as a dead-ball specialist. His 2021/22 campaign was remarkable, scoring twice and registering seven assists in 32 appearances.
The 2015 Hammer of the Year and West Ham United Players’ Player of the Year could be decent value for money at Wolves. He will provide their full-back area with some attacking thrust.
Wolves have already secured the signing of Malian midfielder Boubacar Traore. They will also pay Atletico Madrid £44 million for Matheus Cunha.
Goalkeeper Tom King has also joined on a free transfer following his departure from Northampton Town.
However, they have sold Nathan Collins, Ruben Neves and Conor Coady this summer.