The Indian Express said trends from 250 of the 272 parliamentary seats up for election showed the PML-N was set to win more than 110 seats, while the Pakistan People Party and Imran Khan's Tehreek-i-Insaf Pakistan were winning about 35 seats each.
At home in Lahore, Sharif told supporters to pray that final results, expected to be announced Sunday, would show his party had won an "absolute majority."
"I ask you to pray that the results that come in the morning will show that the PML-N can form government without outside support, so that the PML-N doesn't have to seek support from anyone," he said, the Indian Express reported.
Millions of Pakistanis voted Saturday in the country's first election to mark a transfer of power from one civilian government to another.
The polls closed at 6 p.m., The Nation, a Pakistani newspaper reported. In a few districts in Karachi, the country's largest city, voting stations remained open until 8 p.m. after getting off to a late start.
The campaign has been marred by violence, which continued on election day with at least 17 deaths, The New York Times reported. In Karachi, 11 people died in a bombing at a political office.
It's Pakistan's 10th election since 1970, but the first in which a civilian government has peacefully handed power to a new administration. The balloting also has seen the least interference from the military. It's also arguably seen the most enthusiastic involvement by voters and candidates alike.
Some 4,670 candidates are contesting 272 seats in parliament, and 11,000 people are seeking positions in the four provincial assemblies. For the first time, women ran for office in tribal regions along the Afghan border.
The ballot diversity has attracted voters. At one voting station, 300 women dressed in burqas stood in line. One of them, a 35-year-old doctor, said she had never voted before.
The BBC said long lines of women were seen waiting to vote in Peshawar, along with many first-time voters.
In the run-up to the election, police set up new checkpoints to curb threats from the Taliban to disrupt the voting with suicide bombers. Hospital staff have been put on alert. More than 600,000 soldiers and security forces have been deployed to guard against possible attacks.
The election has not gone without controversy, Dawn News reported.
European Union observers in Lahore said voting was going smoothly. In Karachi, voting was delayed because ballot boxes and voting materials had not yet arrived.