Originally Published: 02 JUN 22 11:41 ET

By Jamie Gangel, Ryan Nobles and Evan Perez, CNN

(CNN) -- The House select committee investigating the January 6 Capitol Hill insurrection has started to reach out to witnesses informing them of the panel's desire to have them appear as part of its upcoming public hearings, which start later this month.

CNN has learned that two people, directly tied to former Vice President Mike Pence, are among those who have received invitations to appear. Former Pence chief counsel Greg Jacob and former federal Judge J. Michael Luttig have received outreach from the committee about their possible testimony.

In addition to Luttig and Jacob, CNN has learned that former Pence chief of staff Marc Short is expected to be called to testify as well.

All three men have already been interviewed privately by committee investigators. In some cases, their testimony has already been used by the committee as part of court filings and subpoena requests of other potential witnesses in their investigation.

Short is one of Pence's closest aides and was with the vice president the entire day on January 6, 2021. He was also a first-hand witness to the pressure campaign applied by then-President Donald Trump and his allies to convince Pence to stand in the way of the certification of the 2020 election.

Jacob was Pence's chief counsel and gave the vice president legal counsel as to how to deal with the request given to him by Trump to prevent the certification. He also pushed back on the advances of conservative lawyer John Eastman, who was among those attempting to convince Trump there was a path for Pence to stand in the way of the certification. In emails obtained by the committee, Jacob was forceful in his denunciation of Eastman's questionable legal theories.

Luttig was enlisted by attorney Richard Cullen, who once served as private counsel to Pence, to knock down Eastman's memo and bolster Pence's argument to Trump that his options to prevent the certification did not exist. Luttig is a prominent former federal judge admired by conservatives and appointed by President George W. Bush. Eastman once worked for Luttig as a law clerk. Luttig made his opinion of Eastman's legal theories known through a lengthy tweet thread that was picked up by news outlets on January 5, 2021. He argued the Constitution did not afford the vice president any power beyond the simple counting of the ballots as they existed. Pence cited Luttig's argument as part of his letter to the nation, outlining his plans to certify the election results. Luttig has said publicly that he is willing to testify.

Luttig declined to comment about the committee invitation. The request for Luttig to appear was first reported by Axios.

Attorneys for Short and Jacob declined to comment on their invites by the committee.

A committee spokesperson declined to comment on potential witnesses for the upcoming hearings.

In addition to testimony from people close to Pence, the committee is also expected to reach out to former officials from the Justice Department who rejected a pressure campaign from Trump allies to use the department to investigate election fraud. The committee has outlined plans for a potential panel of former Justice Department officials, including then-acting Attorney General Jeffery Rosen, his deputy Richard Donoghue and then- Assistant Attorney General Steven Engel. No formal invitations have been issued to those officials but the committee has suggested privately it would hold such a hearing in mid-June.

In addition to the Pence associates and the former Justice Department officials, a source familiar told CNN that the committee will also hear from "first-hand fact witnesses."

The form and fashion of their testimony remains an open question. Committee members are still deliberating the details of their hearings, which topics to focus on and how many sessions will be held. It is expected it will hold between six and eight hearings with at least two planned during primetime hours.

The committee also is planning to use video, audio and other graphic elements at the hearings to help shape the narrative of what led up to the insurrection and what happened on that day.