Mugabe lost control of parliament for the first time since independence in 1980 and the opposition Movement for Democratic Change (MDC) said he had also been defeated in a presidential election last Saturday and should concede defeat. Business Day said Mugabe had privately conceded defeat and was deciding if he should contest a run-off vote needed because MDC leader Morgan Tsvangirai failed to secure a clear majority.
"Mugabe has conceded to his closest advisers, the army, police and intelligence chiefs. He has also told his family and personal advisers that he has lost the election," Business Day quoted an unidentified source as saying.
The newspaper said hardliners in Mugabe's government wanted him to see the contest through to the bitter end, but that personal advisers and his family want Mugabe to quit.
The ruling ZANU-PF and Mugabe's spokesman were not immediately available for comment.
Mugabe, known for his fierce and defiant rhetoric, has not been seen in public since the vote.
In final results of the election for parliament's lower house, the Movement for Democratic Change (MDC) won 99 seats, while Mugabe's ZANU-PF won 97 seats and a breakaway MDC faction won 10. One independent candidate won a seat.
Results for parliament's upper house, the senate, will be issued next.
No official results have emerged in the presidential vote.
Widely blamed for economic collapse of his once prosperous nation, Mugabe has faced growing discontent with the world's highest inflation rate of more than 100,000 percent, a virtually worthless currency and severe food and fuel shortages.
The opposition and international observers said Mugabe rigged the last presidential election in 2002. But some analysts say discontent over daily hardships is too great for him to fix the result this time without risking major unrest.
The mainstream MDC faction said its Tsvangirai had won 50.3 percent of the presidential vote and Mugabe 43.8 percent according to its own tallies.