Franken told the official, who did not want to be identified because Franken has not made an announcement, that he had decided to run in a recent conversation.
"He told me he was running," said the official.
Andy Barr, the political director of Franken's Midwest Values Political Action Committee, declined to comment.
The news was not unexpected. Franken has been calling members of the Minnesota congressional delegation to get their input on a run, and he announced this week that he would be leaving his show on Air America Radio on Feb. 14. He told listeners he would be making a decision on a race soon.
In a swiftly issued statement, Minnesota Republican Party Chairman Ron Carey said he was confident Minnesotans "will reject Franken's divisive, scorched earth attacks."
Should he win the Democratic primary in Minnesota, Franken would take on Republican Norm Coleman, a first-term senator who is among the Democrats' top targets.