While the Judiciary panel is investigating obstruction of justice, the intelligence panel is looking at Russian interference in the 2016 election.
One of the people said the hearing would be delayed a week.
Special counsel Robert S. Mueller III's testimony before Congress might be delayed until July 24, a week later than originally scheduled, to accommodate questioning from more members, multiple media outlets reported Friday.
"At this moment we still plan to have our hearing on the 17th and we will let you know if that changes", said Daniel Schwartz, spokesman for House Judiciary Committee Chairman Jerrold Nadler.
Mueller was scheduled to appear before the House Judiciary and Intelligence committees on July 17 in a much-anticipated public appearance since he gave a short statement following the conclusion of his almost two-year investigation.
The Judiciary Committee also sought to interview former Mueller aides Aaron Zebley and James Quarles behind closed doors. Democrats believed it was agreed to and that Mueller's team may have backed out under pressure from the Justice Department not to participate.
The House Judiciary and Intelligence committees have been negotiating to allow lawmakers more time to grill him. The committees appeared on track to restrict the amount of time that members could speak or which members in attendance might be able to question Mueller.
"Everyone on the committee wants an opportunity to examine Mr. Mueller", said Representative David Cicilline, a senior House Judiciary Democrat.
With just two hours of testimony slotted for each panel, rank and file members of the 41-member Judiciary panel were concerned they might get to play no role, Politico reported.
Mueller's investigation did not find evidence of collusion between Russian Federation and the Trump 2016 presidential campaign.