Speaking at a Congress of SA Trade Unions conference at Midrand, Vavi stressed this was his personal view.
Cosatu had not discussed the issue of President Thabo Mbeki's successor at its conference, but Zuma was clearly "an extremely popular" man, Vavi told Sapa.
The Cosatu congress is aimed at reviewing its contribution to South Africa's democracy, and kick-starting the federation's twentieth anniversary celebrations.
A number of Cosatu affiliate members approached at the event agreed with Vavi's stance on Zuma.
If South Africans looked at Zuma's political credentials they would see he was the man for the job, said a Communication Workers Union provincial secretary who wanted to remain anonymous.
"Irrespective of what the media is saying, I support him becoming the next president. Look, he has been doing the president's job while he (Mbeki) has been out of the country without any problems," he said.
"But we have to remember that he is a human being, and human beings make mistakes. His mistakes should not be politicised."
Reservations have been raised about Zuma becoming the next president due to his allegedly corrupt relationship with his financial adviser Schabir Shaik.
Shaik is expected to shed some light in the Durban High Court this week on an encrypted fax allegedly authorising a R1m bribe for Zuma related to the country's arms deal.
Prerogative of the ANC
An SA Municipal Workers Union international officer said the issue of succession was the prerogative of the African National Congress.
"Cosatu will support the majority view of the ANC. If the ANC wants JZ (Jacob Zuma) we will not oppose the popular view of the ANC," he said.
He said he believed Zuma had the "potential" to make the voices of the workers and the poor heard.
Meanwhile Vavi denied reports that Cosatu has considered breaking away from the tripartite alliance, which also comprises the ANC and SA Communist Party.
He described news reports on the matter as sensationalism, saying he was misquoted.
"There was never a suggestion from any delegate (that Cosatu must split from the Alliance). There was a lot of debate around the issue but it was agreed that we must build the alliance," he said.
Vavi said Cosatu would always be critical when it believed the alliance was not functioning to the best of its ability, but this did not mean that the federation wanted out.
A major concern for Cosatu was that it felt sidelined by the government at times in policy formation.
Delegates interviewed also agreed with Vavi on this matter, saying Cosatu had no ambitions of becoming a political party.