King told reporters after the meeting in Collins' Washington office he might announce Wednesday which party caucus he will join when the new Senate convenes in January, the Portland (Maine) Press-Herald reported. He promised that, whatever his decision, he will work with both Republicans and Democrats.
"The important thing is whichever decision I make ... I don't consider that building a wall between myself and the other party," King said. "When I was a governor as an independent I worked with both parties."
King met Monday with the woman he is replacing, Sen. Olympia Snowe, R-Maine.
Collins said she welcomed King as a "fellow centrist." She added that neither party can expect him to be an automatic vote for their side.
King has been meeting with leaders of both parties. The Senate currently has two independents, Joe Lieberman of Connecticut, who is retiring and being replaced by a Democrat, and Bernie Sanders of Vermont.
The Democrats currently hold a 53-47 edge in the Senate, including Lieberman and Sanders. That will increase by either one or two, depending on King's decision.