Colorado is key to Democratic hopes of retaking a Senate majority in the 2020 election. Senator Chuck Schumer, the minority leader, has spent months trying to recruit Mr. Hickenlooper to enter the contest to face Mr. Gardner. Mr. Hickenlooper would join a Democratic primary that already has 11 declared candidates, including Mike Johnston, a former state senator who placed third in the 2018 Democratic primary for governor; Andrew Romanoff, a former Colorado House speaker; John Walsh, a former United States attorney for Colorado; and Dan Baer, a former Obama administration official.

Mr. Hickenlooper has pooh-poohed his interest in running for the Senate. In February he told reporters in Iowa that he is “not cut out to be a senator.”

Mr. Gardner is seeking a second term in office but faces headwinds in a state where President Trump is highly unpopular. In 2016 Mr. Trump lost Colorado to Hillary Clinton by five points. A July poll of likely Colorado voters from a Republican-aligned firm found Mr. Trump with a 39 percent approval rating in the state and concluded he trails a generic Democratic general election opponent by 12 percentage points.

Democrats must win a net of three Republican-held Senate seats and win the White House to take control of the Senate.

Mr. Hickenlooper in recent weeks has seen an exodus of senior campaign aides, who advised him in the spring to end his presidential bid if his fund-raising and polling status did not improve by the end of July. He qualified and participated in the first two televised debates in June and July, but his performances were not memorable and there has been little improvement in his fund-raising, according to people familiar with his campaign’s finances.

During the three-month fund-raising period that ended June 30, Mr. Hickenlooper raised $1.1 million and spent $1.7 million, an unsustainable pattern for a candidate who has not caught fire with voters. He had $800,000 in his campaign account at the end of June, according to his Federal Election Commission report.

Mr. Johnston and Mr. Baer each raised more campaign funds for their Senate campaigns in the second quarter than Mr. Hickenlooper did for his presidential bid.