"The worst thing [we can] do is go to a congress because we are fighting," Mantashe was quoted as saying. "Basically when you say so, you say: 'Let's fight'.
"...The faction that wins takes it all, and the factions that don't win must disappear and collapse."
According to the report, the African National Congress has set up an eight-member team to help unify its alliance partner, the Congress of SA Trade Unions (Cosatu).
Vavi has been placed on special leave pending the outcome of a disciplinary hearing into an affair he had with a junior employee.
The City Press reported that a survey commissioned by Cosatu and conducted last year, before news of Vavi's affair broke, found that he was popular with both non-Cosatu members and Cosatu affiliates.
The survey of 3 030 workers, which was conducted by the Community Agency for Social Enquiry, did not sample respondents to reflect the size of the unions to which they belonged.
The Sunday Times reported that there was doubt within Cosatu leadership about whether a special congress would be called. It was requested by nine of the 19 Cosatu-affiliated unions.
Cosatu's central executive committee (CEC) has asked its president Sidumo Dlamini to report on the feasibility of convening the special congress.
Cosatu vice-president Zingiswa Losi said the matter of calling the congress, which could result in ordinary members reinstating Vavi, was not "cut and dry", and the CEC meeting in November would have the final say.
According to The Sunday Times, if the congress was boycotted by the affiliates which opposed Vavi boycotted, the could be problems achieving the quorum needed for decision-making.