The Washington Post said Murkowski appeared to have a solid lead.
About 89 percent of ballots that had been counted through Thursday were clearly for Murkowski, who waged a write-in campaign as an independent to keep her seat after losing to Republican candidate Joe Miller in the primary, the Post reported Friday.
Miller challenged hundreds of ballots because of misspellings and other issues.
Election officials said about a third of the approximately 92,000 write-in ballots had been counted and anticipated the process would last several more days.
In the Nov. 2 election, the Tea Party-backed Miller captured 35 percent of the vote and 40 percent of the voters wrote in their selection.
Miller has argued that election officials must toss ballots that have Murkowski's name misspelled. But state officials said the law does not have such a strict standard and they will accept minor misspellings if the voter's intent is clear.
"Given the current trends, the actual number of ballots that have misspellings, with that number we would still have a margin of victory," Kevin Sweeney, a Murkowski campaign spokesman, told the Post.
Miller campaign volunteers monitoring the ballot-counting have been watching for misspellings of Murkowski's name but also have challenged ballots that say "Murkowski, Lisa" or "Lisa Murkowski Republican," and ballots that seem to be perfect, the Post said.
The tactic has drawn criticism from several groups, but a Miller campaign spokesman said volunteers were acting appropriately in challenging ballots so they receive further scrutiny.
"Right now, we just want the law upheld and clarified, and we're segregating all the challenged ballots for review," said Randy DeSoto, a spokesman for Miller's campaign.