The ZESN, which deployed 8,000 local election observers, estimates that Tsvangirai won 49.4 per cent of the votes against 41.8 per cent for Mugabe, the current president.
If those results were confirmed a second round run-off would have to be held to decide the presidency.
An official in Mugabe's Zanu-PF told the AFP news agency that the president "doesn't want to embarrass himself by going to a run-off".
"There is only one person still blocking him, the army chief of staff," the official, speaking on condition of anonymity, reportedly said.
At a news conference late on Tuesday, Tsvangirai said that there were no discussions with Zanu-PF and he was still waiting for official results from the election commission.
However, it was clear that he remained confident about the MDC's chances in the presidential and parliamentary contests.
"After the 29th of March, Zimbabwe will never be the same again. In those minutes inside the polling booths each one rewrote the history of Zimbabwe," he said.
"The vote we passed on Saturday was a vote for change, for a new beginning."
The Associated Press news agency reported that sources close to the two rivals had told them that advisers to Mugabe and Tsvangirai were meeting after the president was told he was trailing far behind the opposition leader.
Mugabe was told there could be an uprising if he were declared the winner, it reported.
Earlier, Tendai Biti, secretary-general of Tsvangirai's party, had told Associated Press that the report was "rubbish".Contemplating defeat
Slovenia, which holds the European Union's rotating presidency, has urged Mugabe to step down.
"If Mr Mugabe continues, it will be a coup d'etat," Dimitrij Rupel, Slovenia's foreign minister, said after addressing the European Parliament.
|Mugabe has ruled Zimbabwe since |
independence 28 years ago [AFP]
"I hope he is on his way out, most Europeans think this way."
Marwick Khumalo, head of the Pan-African Parliament observer mission, told South African radio on Tuesday that leading members of Mugabe's party were contemplating defeat with trepidation.
"I was talking to some of the big wigs in the ruling party and they also are concerned about the possibility of a change of guard," Khumalo said.