The Midlands club are still interested in the former Manchester United man, who is available on a free, despite his chronic knee problems.
Albion have already been in contact with Hargreaves although manager Roy Hodgson is likely to be wary of signing a player who has played only 27 games in the last four seasons.
However Hodgson is still interested in bringing the 30-year-old to The Hawthorns and discussions over the player’s fitness and future will take place in America over the next week.
The Baggies are likely to offer Hargreaves a play-as-you-play deal with the likelihood of an extension if he reaches a certain amount of games.
If the ex-England international can remain fit for a substantial amount of games it would prove to be a real coup for Hodgson as he looks to consolidate West Brom’s Premier League position.
His experience not only on the pitch but also in the dressing room could prove invaluable to Hodgson and his side as they look to push on from last seasons 11th place finish.
Hargreaves won 42 caps for the national side, playing in the 2006 World Cup, also winning a Chamions League medal at both Bayern Munich and United.