Mercedes driver Nico Rosberg made the offer after the pair clashed during the winners’ press conference following the season’s first race in Australia.
But Vettel said the initiative was a thinly veiled public relations exercise.
“Now they use it as a PR thing… so the answer is ‘no’,” he told reporters at Malaysia’s Sepang circuit.
“I think I’m pretty busy here, so I’m better off staying here,” Vettel added.
Rosberg’s offer came after a tasty exchange in Melbourne, in which Vettel mocked his fellow German’s insistence that runaway Mercedes would welcome greater competition.
“So, you hope you slow down, is that what you’re saying?” Vettel shot back at the time.
On Thursday, he insisted he was better off spending time in Ferrari’s garage rather than posing for the cameras with Rosberg and Lewis Hamilton.
“Imagine if I go there, do you think they would really open up? If I go, I think it’s all staged,” Vettel said.
He added: “There’s always something you can learn from other people but I think we have a lot of intelligence in our team.”
The four-time world champion finished third in Australia on his debut drive for Ferrari, some distance behind the Mercedes cars of Hamilton and Rosberg.