The 29-year-old spent the last season on loan at Newcastle United where he enjoyed the best season of his career in the Premier League.
He scored 11 goals and provided seven assists, and played a major role in helping the Magpies stay in the Premier League.
Newcastle are keen to sign him permanently and have offered less than £10m, which is some way off West Brom’s valuation of the player.
West Ham are willing to match the fee, but the Baggies are still holding out for his £16.5m release clause fee.
However, the report claims that the Hammers are leading the battle to secure the services of the 77 times capped Venezuela striker.
With Newcastle now unlikely to return with a bid following Benitez’s departure, West Ham have a great opportunity to land the striker.
The Hammers are desperate to sign a striker after Andy Carroll has been released by the club, and with Javier Hernandez contemplating his future.
Rondon has loads of Premier League experience and would be a decent signing for the club.