Mrs. Clinton’s successor in the Senate, Kirsten E. Gillibrand, has paid more than $1 million this year through her political committees to a top online fund-raising firm, which has helped her reap $2.3 million this year in small donations for a 2018 re-election race in which she is the heavy favorite. She has also continued courting major donors, holding two fund-raisers last month in the Hamptons. At one, she was asked by a donor whether she was considering running for president. She said she was focused on 2018, but did not explicitly rule out a White House run, according to an attendee.

Gov. Terry McAuliffe of Virginia, a former chairman of the Democratic National Committee who maintains deep ties to some of the party’s most generous donors, has spent $164,000 through his political committee on staff members and consultants this year, and $46,000 in recent months to hold fund-raisers and other events at a Washington steakhouse. The PAC, which rents office space in Washington, this year collected big checks from longtime backers of the Clintons, including $50,000 from Howard Kessler, a Boston financier, and $25,000 each from the Virginia real estate developer Albert J. Dwoskin and from Douglas J. Band, a former Clinton aide and fund-raiser. The PAC has also donated more than $315,000 to Democratic candidates and committees in Virginia this year.

Mr. McAuliffe — who is barred by term limits from running in the Virginia governor’s race this year — said during an appearance Sunday on CNN that he got asked “all the time” whether he was running for president. “We’ll see what happens down the road. But I have no intentions of running for president,” he said, explaining that his focus was on finishing his governorship and helping the party’s gubernatorial candidates in 2018.

Aides to Ms. Gillibrand and those of other prospective candidates contacted for this article similarly insisted that their fund-raising had nothing to do with setting the stage for 2020.

It is considered bad form to start running for president — or even to unofficially explore the possibility — before the preceding midterm election. That is partly because presidential campaigns can divert valuable funds away from important down-ballot races for which it is more difficult to raise money.

There are also tactical advantages to waiting, including keeping open the possibility of remaining in Congress in states that bar members from seeking re-election while also running for another office. And campaign finance regulations limit the types and amounts of money that declared presidential candidates can raise, while politicians who have not declared for the presidency can continue accepting larger contributions to a range of political committees, including state-level committees like the one used by Mr. McAuliffe.