Paulista has yet to play for the Hammers since joining on loan last month but has scored in three successive matches for the development squad.
Hammers boss Sam Allardyce reportedly offered the forward a place on the club's six-day training camp in Dubai but he has decided to stay in East London and play a full match for the reserves against Southampton.
A club insider told The Sun: "Everyone was a bit surprised to hear about Wellington turning down the chance to go.
"He plays for a top-six side in Brazil but has come to West Ham to prove himself. And he is happy to play in front of 300 fans for the reserves to do so. He's 28 and in his youth scored against Barcelona at the Nou Camp so he knows what the big time is.
"He says staying here will help make him fitter and reckons playing for the reserves will get him fitter than going to Dubai. This boy could surprise a few people."
West Ham are in Dubai on the back of a fifth successive Premier League defeat at Aston Villa last weekend.