The Daily Mirror is reporting that both of the London clubs are keeping tabs on the Venezuela international, who has a £16m buy-out clause in his contract following West Bromwich Albion’s relegation from the Premier League.
West Ham are also believed to be keeping tabs on the 28-year-old’s situation as the Hammers look to strengthen their squad following the appointment of Manuel Pellegrini as the club’s new manager.
Rondon was a key player for the Baggies last season but he was unable to prevent West Brom from being relegated from the top flight.
He scored seven goals and made three assists in 36 Premier League games for the Baggies before they dropped down to the Championship.
Chelsea FC are believed to be on the lookout for a number of new signings this summer as they look to bounce back into the Champions League spots next season.
The Blues ended up in fifth place in the Premier League table as they missed out on qualification for the Champions League, but they did manage to beat Manchester United in the FA Cup final to end the campaign with a trophy.
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