Franken, 66, a former comedian who had been seen as a rising star in the Democratic Party, was set to make an announcement on the Senate floor at 11:45 a.m. (1645 GMT).
CNN cited unnamed sources as saying he would announce he was stepping down.
The departure of the Minnesota Democrat would present an opening for Republicans to recapture a seat they lost when Franken won election in 2008, and to build on their slim 52-48 Senate majority.
The election to succeed him, however, would not be held until November 2018. In the interim, Minnesota’s Democratic governor, Mark Dayton, would appoint someone to take his place, ensuring Democrats hold the seat for now
Franken is one of several prominent American men in politics, media and entertainment to be accused in recent months of sexual harassment and misconduct.
Allegations he had groped and tried to kiss women without their consent began to surface three weeks ago.
After the initial accusations, Franken apologized, saying he would stay in office, cooperate with a Senate ethics probe and work to regain the confidence of Minnesota citizens.
A majority of his Democratic Senate colleagues, including most of the party’s female lawmakers in the chamber, pressed him to step down on Wednesday after a new allegation hit the news.
Politico reported that a congressional aide said Franken had tried to forcibly kiss her in 2006, before he was elected to the Senate. Franken denied the allegations, Politico reported.