Special Counsel Robert Mueller’s appearance before a House panel has been stalled partly due to discussions on whether the White House’s assertion of executive privilege would limit his testimony, according to people familiar with the matter.

The House Judiciary Committee and Mr. Mueller’s team have been in negotiations for days about the contours of the special counsel’s eagerly-awaited testimony about his 448-page report on Russian interference in the 2016 election and episodes in which President Trump allegedly sought to...