Aides to former Vice President Joseph R. Biden Jr. are discussing the possibility of seeking an alliance with Senator Amy Klobuchar in next week’s Iowa caucuses, a plan that would involve a pledge to help each other in precincts where one of them does not have enough support to win delegates.

Three staff members for Mr. Biden’s Iowa campaign tentatively floated the idea to a top Klobuchar adviser at a meeting this week, according to Democrats briefed on the meeting.

People in both the Biden and Klobuchar camps played down the discussion, which took place at a Des Moines restaurant, and aides for Ms. Klobuchar said they did not regard it as a serious overture. But there is little doubt among Mr. Biden’s allies in the state that his campaign is contemplating such steps, with an eye toward preventing a messy split among moderate candidates on Monday.