The Mirror report that the Venezuela international can be signed for £16m thanks to a clause in his contract that became active upon Albion's tumble into the Championship, which could spark a tussle between a number of clubs.
Chelsea and Tottenham were said to be interested back in January, and Premier League new boys Cardiff City are also sniffing around now as they try to strengthen ahead of their return to the top flight.
A possible reason why West Ham are now in the mix is because of Tuesday's official announcement that Manuel Pellegrini is the new manager of the club.
The Hammers decided against giving David Moyes a new deal despite him leading them to a 13th place finish in 2017/18, and have instead appointed former Manchester City boss Pellegrini on a three-year deal.
The 64-year-old used to manage Malaga, and knows all about the qualities Rondon can bring to a side having worked closely with him.
West Brom are likely going to have to balance the books following their relegation, and Rondon is one of the likeliest to leave, as is Jonny Evans.
Should he sign, the fans will be hoping to see him team up well with his old boss Pellegrini - over the years, the Irons have gone through a high number of strikers with very few being able to lay claim to have been a success.