The White House and the Justice Department have begun drafting court documents seeking to overturn subpoenas issued to President Reagan and Vice President George Bush for their courtroom testimony in the Iran-Contra conspiracy trial of Oliver L. North, administration officials said Saturday. Their comments came amid reports that several other senior government officials had been or would soon be subpoenaed to testify as witnesses in the trial of North, a former White House aide who was the central figure in the Iran-Contra affair.

Federal law-enforcement officials said they expected announcements shortly that defense or prosecution subpoenas had been issued to Secretary of State George P. Shultz, former Attorney General Edwin Meese III and current and former officials of the National Security Agency and Central Intelligence Agency, possibly including the CIA director, William H. Webster. Administration officials said the decision by the White House to fight the subpoenas issued to Reagan and Bush had been made even before the documents were delivered to the Justice Department on Friday.Within the next week, they said, White House and Justice Department lawyers are expected to file a motion in Federal District Court here to quash the subpoenas.

The officials appeared confident that Reagan and Bush would prevail in their arguments that because of constitutional protections accorded to the executive branch, the two men cannot be compelled to make a courtroom appearance. No sitting president has ever appeared as a courtroom witness in a criminal trial.

Aides to the president and president-elect did not to rule out the possibility that Reagan and Bush would provide videotaped depositions that could be replayed in the trial or would answer written questions.

Other presidents have provided videotaped depositions in criminal cases, and legal scholars suggested that a similar procedure was likely to be used in the trial of North, who has been indicted on charges that he conspired to defraud the United States by illegally providing Nicaraguan reb-el groups with proceeds from the sale of U.S. weapons to Iran.

The trial is to begin Jan. 31.