The unofficial result came after the Secretary of State's Office counted 933 absentee ballots, the (Minneapolis) Star-Tribune reported. Franken was ahead by 49 votes out of almost 3 million cast before the absentee ballot count, and picked up an additional 176 votes.
Coleman's term in the Senate expired Saturday.
Lawyers for Coleman have asked the state Supreme Court to order another 2,000 rejected absentee ballots into the count, and the court has not yet said when it would rule.
Regardless of which candidate comes out on top in the final count, the other is expected to sue.
Franken, who grew up in Minnesota, gained national prominence as a writer and performer on "Saturday Night Live" and has long been active in Democratic politics. Coleman won a narrow victory over former Vice President Walter Mondale six years ago after incumbent Democratic Sen. Paul Wellstone was killed in a plane crash shortly before the election.