Tsvangirai, who leads the Movement for Democratic Change (MDC), has already said that he has won the presidential election outright.
He says that Mugabe, who leads the Zanu-PF party, has delayed the results of the presidential poll in order to rig the election.
Mugabe will be declared the winner of the presidential poll if Tsvangirai decides not to take part in a run-off vote, according to election rules.
A senior Zanu-PF party official said that the figures suggested by the government sources had credibility.
"Those figures are in line with the official figures and the MDC knows that the official tally is more or less around that but they have been inflating their numbers to claim a false victory," the official said.
Another source said that Tsvangirai had in fact taken a higher proportion of the vote, between 48 per cent and 50 per cent, while another said the opposition leader had won more than 47 per cent "but less than 50" per cent.
The electoral commission is due to start a collation and verification process on Thursday.
Mugabe's chief spokesman George Charamba said he was not aware of the figures leaked by government sources on Wednesday.
"I was with [electoral commission chairman] Justice [George] Chiweshe yesterday and he was waiting for results from different centres," he said.
The MDC and human-rights groups say that Zanu-PF has led a violent campaign to intimidate Zimbabweans into voting for Mugabe in a run-off.
The government has dismissed the accusations.
The presidential vote in Zimbabwe was held simultaneously with parliamentary and senate polls, amid a worsening economic crisis.
The Zanu-PF party has already lost control of the 210-seat parliament after results of that poll were released.
The country is experiencing severe food, fuel and foreign currency shortages.
Its current rate of inflation - 165,000 per cent – is the world's highest.