The Sunday Mirror says following the club's sixth straight defeat, against Stoke, Zola met Sullivan and Gold for crisis talks last Saturday night and vowed he was the man to lead them out of trouble.
He said he wanted to battle on but just 30 minutes later contradicted himself, claiming he was considering his future.
Zola's decision to return home to Sardinia for three days last week to film a TV commercial infuriated Sullivan, who felt he should have remained in England to address the growing crisis at the club.
Zola then publicly contradicted his club's decision to complain to the Premier League over Fulham fielding a weakened team in their defeat by Hull.
Increasingly the Hammers' hierarchy believe Zola is trying to undermine his own position in order to claim a £3million pay-off.