Rondon is expected to leave the Baggies following their relegation from the Premier League, with the Venezuelan available for £16m due to a buyout clause in his contract.
Chelsea remain keen to bring in a target man during the current transfer window despite signing Olivier Giroud in January, while Spurs are also looking for a suitable back-up to Harry Kane with Fernando Llorente expected to leave the club this summer.
The Mirror reports that both clubs have identified Rondon as a possible option, but could face competition from fellow London rivals West Ham United.
Rondon scored 10 goals in 39 appearances for West Brom across all competitions last season, including seven in 37 Premier League outings.
Baggies boss Darren Moore is eager to keep as much of his squad together in a bid to earn an immediate return to the top flight, but is understood to be resigned to losing Rondon, Jonny Evans and Kieran Gibbs.