Johnstone made his Premier League debut last season with the Baggies, and he had an impressive campaign despite the Midlands outfit being relegated.
The shot-stopper has told his close friends that he would like to make an instant return to the English top-flight with David Moyes’ side.
Johnstone has 13 months remaining on his contract, but he won’t come on the cheap with a reported price tag of around £20 million.
The 28-year-old made more saves than any other goalkeeper in the top-flight (166) with an impressive save success rate of 70.6 percent.
Tottenham Hotspur have reportedly been linked with his services, but Johnstone would only act as a back-up with Hugo Lloris set to stay for another campaign.
A return to Manchester United also appears unlikely with the fierce competition from David de Gea and Dean Henderson for the shot-stopper’s role.
His best chance of claiming the number one spot could be with the Hammers. Lukasz Fabianski is already 36, and he has a good chance of taking the gloves.
The Hammers will be playing Europa League football next term. It will be their first-ever group stage appearance in the European competition.
Moyes will need to rotate his goalkeeping options. If Johnstone joins them, he could initially feature in the competition before establishing himself as a league regular.
Stats from Transfermarkt.com and Fbref.com