The 25-year-old, a boyhood Hammers fan, joined the club from Ipswich Town for around £12m in the summer of 2022 and made 35 appearances across all competitions.
However, Downes only started seven times in the 2022-23 Premier League season and the decision was made to send him out on loan to Southampton last summer in search of regular first-team football.
The defensive midfielder established himself a key cog in Russell Martin's machine as the Saints finished fourth in the Championship table before beating Leeds United 1-0 in the playoff final to secure promotion back to the top flight at the first attempt.
Downes played 37 times for Southampton last season, including 35 starts, and the Brentwood-born midfielder now looks set to continue his career at St Mary's.
Downes to undergo Southampton medical
According to Sky Sports News reporter Dharmesh Sheth, Southampton have agreed a deal with West Ham for the permanent signing of Downes, with the fee understood to be worth £18m.
Sheth adds that Downes has left West Ham's pre-season camp in Austria after being given permission to undergo a medical with Southampton in the UK.
The Saints have already experienced a busy summer transfer window and Downes could soon become their eighth permanent signing.
Taylor Harwood-Bellis played alongside Downes at Southampton last season and has made his move to St Mary's permanent for £20m following a successful loan spell from Manchester City.
Yukinari Sugawara, Nathan Wood, Ronnie Edwards, Charlie Taylor, Rento Takaoka and Adam Lallana have also made the move to Southampton this summer.
Why are West Ham letting Downes go?
Although Downes is rated highly by West Ham, the midfielder does not seem to feature in the first-team plans of new head coach Julen Lopetegui.
The Hammers are already well stocked in the midfield department, with James Ward-Prowse, Edson Alvarez and Tomas Soucek three first-team stars expected to feature regularly next season.
Lucas Paqueta, who has been linked with a return to his native Brazil, is another who is comfortable operating in midfield, while academy graduate George Earthy will hope to gain more first-team opportunities after breaking into the senior side at the end of last season.
West Ham are set to use the funds generated from the sale of Downes to recruit new players, with Lopetegui's side having already signed Max Kilman, Luis Guilherme and Wes Foderingham this summer.