The House select committee investigating the Capitol attack is considering issuing a subpoena to Ivanka Trump to force her cooperation with the inquiry into Donald Trump’s efforts to return himself to power on 6 January, according to a source familiar with the matter.

Any move to subpoena Ivanka Trump and, for the first time, force a member of Trump’s own family to testify against him, would mark a dramatic escalation in the 6 January inquiry that could amount to a treacherous legal and political moment for the former president.

The panel is not expected to take the crucial step for the time being, the source said, and the prospect of a subpoena to the former president’s daughter emerged in discussions about what options remained available after she appeared to refuse a request for voluntary cooperation.

But the fact that members on the select committee have started to discuss a subpoena suggests they believe it may ultimately take such a measure – and the threat of prosecution should she defy it – to ensure her appearance at a deposition on Capitol Hill.

The select committee did not address a possible subpoena for Ivanka Trump at a closed-door meeting last Friday, and the panel wants to give her a reasonable window of opportunity to engage with the investigation before moving to force her cooperation, the source said.

The panel would also have to formally vote to move ahead with such a measure, the source said, and Thompson would probably inform the House speaker, Nancy Pelosi, of the decision before formally authorizing a subpoena to the former president’s daughter.

But members on the select committee are not confident that Ivanka Trump would appear on her own volition, the source said, and the discussion about a subpoena reflected how important they consider her insight into whether Trump oversaw a criminal conspiracy on 6 January.

The chairman of the select committee, Bennie Thompson, said in an 11-page letter requesting her voluntary cooperation last month that the panel wanted to ask about Trump’s plan to stop the certification of Joe Biden’s election victory to return himself to office.

Ivanka Trump was close to the former president in the days leading up to the Capitol attack, Thompson said, and appeared to have learned the plan to have the then vice-president, Mike Pence, refuse to certify Biden’s election win in certain states was possibly unlawful.

“The committee has information suggesting that President Trump’s White House counsel may have concluded that the actions President Trump directed Vice-President Pence to take would … otherwise be illegal. Did you discuss these issues?” the letter said.

The letter added House investigators had additional questions about whether Ivanka Trump could say whether the former president had been told that such an action might be unlawful, and yet nonetheless persisted in pressuring Pence to reinstall him for a second term.

Thompson also said in the letter that the panel wanted to learn more about Trump’s indifference to the insurrection, and discussions inside the White House about his tweet castigating Pence for not adopting his plan as a pro-Trump mob stormed the Capitol in his name.

The letter said a persistent question for Ivanka Trump – who White House aides thought had the best chance of persuading the former president to condemn the rioters – was what she did about the situation and why her father did not call off the rioters in a White House address.

The select committee said in the letter that they also wanted to ask her about what she knew with regard to the long delay in deploying the national guard to the Capitol, which allowed the insurrection to overwhelm law enforcement into the afternoon of 6 January.

Thompson said that House investigators were curious why there appeared to have been no evidence that Trump issued any order to request the national guard, or called the justice department to request the deployment of personnel to the Capitol.

A spokesperson for the select committee declined to comment on whether the panel was considering a subpoena for Ivanka Trump or the content of the Friday meeting. Neither a spokesperson for the former president nor Ivanka Trump responded to requests for comment.

But Ivanka Trump has appeared to suggest she is not prepared to appear voluntarily, and said in a statement at the time of the letter requesting voluntary cooperation that “as the committee already knows, Ivanka did not speak at the January 6 rally”.