The adoption of the U.S. Constitution.

Certain officials in the Roman Republic, e.g. consul and proconsul, had imperium, which included an immunity from prosecution while holding office. I know that many of the architects of the Constitution were students of ancient Rome and specifically tried follow or avoid certain features of the Roman constitution.  Is there any evidence in the records of the Constitutional Convention, the ratifying debates, the Federalist papers, or elsewhere indicating that a similar immunity from prosecution while in office was considered or discussed? Obviously, this question is prompted by the DOJ's opinion that a sitting President cannot be indicted.