This after building what appeared to be an unassailable lead against his closet rival, a local newspaper reported on Friday.
The independently owned Post newspaper said Patriotic Front (PF) candidate Lungu led Hakainde Hichilema by about 33,000 votes with 30,000 votes yet to be counted from just one more constituency.
With no reliable opinion polls in the southern African state, few experts have been keen to call a winner in the contest to succeed Michael Sata, who died in office in October aged 77.
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“The margin is small but it has definitely given us a winner,” the newspaper said.
The Electoral Commission of Zambia is due to give the final result on Friday.
Voter turnout in the copper-rich south African state was around 34 per cent as heavy rains disrupted voting across much of the landlocked country. Observers said the election was conducted in a fair manner.