GOP Rep. Mike Simpson is a former president of the House of Representatives.
Former presidents, former vice presidents, and presidents-elect are also eligible.
If Simpson were to be impeached for the same reason, he would have to resign.
Simpson was indicted for allegedly violating campaign finance laws and tax laws.
He faces up to 15 years in prison.
Republicans have been pressing the House to impeach President Donald Trump for years.
The impeachment process has been delayed for months because of the Russia investigation, but the House voted overwhelmingly to approve impeachment.
The vote on the House floor is expected on Thursday.