The former Wolves man is thought to be surplus to requirements at Upton Park after two seasons, with the Hammers’ summer transfer business having upped competition for places.
Baggies chief Alan Irvine has been alerted, and is keen to make the former England international one of his Hawthorns stars.
The Hammers are understood to be ready to take a hit on the £7.5m paid for the wide-man, who has not hit the heights expected of him after his impressive spell at the Molineaux.
West Brom are confident that they can revive the 28-year-old’s career, as they set about ensuring another season in the top tier.
Jarvis has only managed four goals in 57 outings for the Irons, which has seen him slip away from the England set-up – he has one cap to his name earned in 2011.