In addition to Potter, West Ham also spoke to former AC Milan boss Paulo Fonseca and ex-Paris St-Germain manager Christophe Galtier, currently in charge of Saudi Pro-League club Al-Duhail.
The 49-year-old Potter, though, will return to management for the first time since he was sacked by Chelsea in April 2023.
He was their first managerial appointment following Todd Boehly’s takeover at Stamford Bridge, but dismissed after less than seven months in charge.
Chelsea paid more than £21m in compensation to Brighton, where Potter had impressed after leading the Seagulls to Premier League finishes of 15th, 16th and ninth in a three-year spell.
Potter, who has also managed at Ostersunds FK and Swansea City, oversaw a record £323m outlay at Stamford Bridge in the 2023 January transfer window, but success did not materialise and he was sacked following an 11th defeat in 31 games.
He was also linked with the England job before Thomas Tuchel, his predecessor at Chelsea, was appointed as Gareth Southgate’s successor.
In an interview with the Telegraph, Potter said club football was “more rewarding” than international management.