The announcement from the Judiciary Committee comes as lawmakers on that panel and the House Intelligence Committee are preparing to hear directly from Mr. Mueller himself next week for the first time. The former special counsel resisted testifying but ultimately agreed to back-to-back, two-hour public hearings with the committees.

Democrats hope the sessions will bring Mr. Mueller’s dense 448-page report to life and ignite public interest in the 10 or so episodes of possible obstruction of justice by Mr. Trump that the investigation documented. Republicans will be pressing another of Mr. Mueller’s conclusions: that his team did not find the evidence to bring a case that Mr. Trump’s campaign conspired with the Russians to undermine the 2016 election.

The new subpoenas related to the committee’s investigation of possible obstruction of justice and abuse of power by Mr. Trump would position Democrats to try to capitalize on any momentum Mr. Mueller may provide. They target former law-enforcement and White House officials and individuals connected to hush-money payments during the 2016 campaign, part of efforts aimed at buying the silence of a pornographic film actress and of a Playboy model who claimed to have had affairs with Mr. Trump.

Many of the subjects of possible subpoenas have intimate knowledge of either the Trump campaign’s contacts with Russia during Moscow’s attempt to subvert the 2016 election or Mr. Trump’s later efforts to impede federal investigators trying to untangle those ties, by trying to fire Mr. Mueller, curtailing his investigation or taking other steps.

Other former officials include Jody Hunt, Mr. Sessions’s chief of staff who took detailed notes of interactions with the president, and Rick A. Dearborn, a Sessions confidant who served on the Trump campaign and in the White House. The committee will also authorize subpoenas for Jared Kushner, Mr. Trump’s son-in-law and White House adviser.

If the committee votes to authorize the subpoenas as expected, Mr. Nadler will have the discretion to decide when to issue them.

The committee has already authorized but not yet used subpoenas for Reince Priebus, Mr. Trump’s first chief of staff, and Stephen K. Bannon, who helped run his presidential campaign and was an architect of the early days of his presidency.