Ramsdale joined Southampton from Arsenal last summer for 18 million pounds but endured a torrid season as the Saints were relegated with just 12 points - narrowly avoiding Derby County's infamous all-time low of 11.
Despite conceding 66 of Southampton's 86 league goals in 2024-25, Ramsdale remains a player of interest for Premier League clubs, and West Ham have emerged as the front-runners.
The Hammers, now under the management of Graham Potter, are keen to bolster their options between the posts following the departure of long-time keeper Lukasz Fabianski after seven seasons.
Although Alphonse Areola remains at the London Stadium, he too suffered a difficult campaign as West Ham conceded 62 goals - the sixth-highest in the division - during their 14th-place finish.
Southampton are open to selling Ramsdale, eager to shed his 100,000-pounds-a-week wages as they regroup in the Championship.
The club is reportedly holding out for 20 million pounds, a modest increase on what they paid Arsenal less than a year ago.