(CNN) — Former President Donald Trump has appealed a judge’s order that former Vice President Mike Pence must testify to a federal grand jury investigating the 2020 election aftermath but hasn’t gotten a court’s intervention to block Pence from testifying, according to a person familiar with the case.

Trump’s attempt to claim executive privilege around their conversations is considered a long shot, given that the former president has lost several attempts in court to block other top officials from his administration from testifying.

Pence has said he would not appeal the judge’s order from late March and would comply with his subpoena. He could be called before the grand jury as early as this week.

Sealed filings in the DC Circuit Court of Appeals related to Trump’s appeal came in on Monday and do not indicate Trump is seeking any emergency intervention at this time, though one of his lawyers was spotted at the courthouse on Monday.

Separate from Trump’s executive privilege arguments, Pence had argued he should be covered by the Constitution’s Speech or Debate Clause, which shields lawmakers from certain law enforcement actions connected to their legislative duties.

The judge decided Pence must testify about conversations where Trump may have been acting corruptly, but Pence could still decline to answer questions related to January 6, 2021, when he was serving as president of the Senate for the certification of the 2020 presidential election.

Trump files long-shot appeal of judge’s order for Pence to testify in January 6 probe