The news outlet claims that Fulham are also interested in the 21-year-old, who impressed while on loan at Oxford United last season but is in the final year of his contract at the London Stadium.
It is understood that Manuel Pellegrini will take a close look at Browne during the Hammers’ pre-season training, but he is attracting plenty of attention from across the UK.
Good move for Rangers?
Steven Gerrard needs to improve his squad this summer, but he should only really be looking to sign players who are better than the players that would normally play in his starting line-up.
Browne is a versatile attacker who can play on both wings or in a central attacking midfield role.
If the Gers can re-sign Ryan Kent then that’s their left wing option sorted, but on the right wing, Daniel Candeias is someone who needs to be improved upon.
Browne scored nine goals and supplied five assists in 44 appearances across all competitions for League One side Oxford United last season.
He could put pressure on Candeias for that spot in Gerrard’s line-up, but he is not the major upgrade that is needed.
This is Futbol rating 6/10
Likely to happen?
It is hard to tell at the moment because Browne’s future seems to hinge on whether or not Pellegrini is impressed by him in the Premier League club’s pre-season training.
And even if he fails that and goes up for sale, Fulham and Celtic probably stand a better chance of signing the in-demand attacker than Rangers.
This is Futbol rating 2/10