The agreement to delay the hearings in exchange for an extended testimony is not complete, the sources say, and lawmakers are still negotiating.
Mueller has been scheduled to appear on July 17 before the court and intelligence committees in the back-to-back sessions where 22 members from each committee would be considered for special councils.
Presidency chairman Jerry Nadler's spokesman Daniel Schwarz said: "" Right now we are still planning to get our hearing on the 17th and we will announce if it changes. "
On Friday morning, the Judiciary Committee took an abnormally brief recess from a hearing on the Mueller report so members can be informed of the discussions.
This story has been updated with further developments Friday.