The article reported that a number of Republicans appeared to be positioning themselves to run in 2020 as the president endures low poll numbers and faces multiple investigations into whether his associates had contacts with Russia during last year’s campaign. While some might take on the incumbent president of their own party, the article reported that multiple advisers to Mr. Pence had intimated to party donors that he would plan to run if Mr. Trump did not seek re-election.

In one June meeting, an aide to the vice president, Marty Obst, said Mr. Pence’s team wanted to be prepared to run in case there was an opening in 2020, according to a Republican briefed on the meeting. Nick Ayers, the vice president’s new chief of staff, has signaled to major Republican donors that Mr. Pence wants to be ready, the article reported.

The article quoted Mr. Obst denying that he and Mr. Ayers had made any private insinuations. He also called suggestions that the vice president was positioning himself for 2020 “beyond ridiculous.”

Mr. Pence has set up a political fund-raising organization, Great America Committee, and has hosted key figures at the vice president’s mansion, like Tony Perkins of the Family Research Council and representatives of Charles G. and David H. Koch, the billionaire conservative financiers. Last month, the vice president hosted Kelly and Joe Craft, coal barons from Kentucky.

A top White House official said Sunday that there would be no reason for the vice president to prepare his own White House bid because Mr. Trump planned to run. “The president says privately and publicly often, George, that he’ll be there for seven and a half more years. So he plans on being a two-term president,” Kellyanne Conway, the president’s counselor, told George Stephanopoulos on “This Week” on ABC. “It is absolutely true that the vice president is getting ready for 2020, for re-election as vice president.”