Schiff, the likely incoming chairman of the House Intelligence Committee, told CNN's Wolf Blitzer that he believes that the DOJ's position, reflected in an opinion of the department's Office of Legal Counsel, should be given another look if it is found that following it would allow someone to escape justice.
"I think the Justice Department needs to reexamine that OLC opinion, Office of Legal Counsel opinion, that you cannot indict a sitting president under circumstances in which the failure to do so may mean that person escapes justice," Schiff said.
"If it were the case that it was now or never ... that if you wait until after the president leaves office they can no longer be brought to justice, that ought to create certainly an exception to that OLC rule," Schiff said.
He added that the Office of Legal Counsel should consider "revisiting and revising the rule altogether."
Federal prosecutors in a legal filing last week appeared to refer to Trump as "Individual-1," who it said had directed Michael Cohen, Trump's former personal attorney, to make illegal payments to two women claiming they had affairs with Trump.
The DOJ's Office of Legal Counsel has maintained since the Nixon administration that a sitting president cannot be indicted. That position was reaffirmed during the Clinton administration, but it has never been tested in court.
Blitzer asked Schiff if he is suggesting that the DOJ "indict [Trump] now and maybe try him after he leaves office."
"I don’t think the Justice Department ought to take the position — and it’s certainly not one that would be required in any way by the Constitution — that a president merely by being in office can be above the law, can escape the enforcement of the law, by essentially waiting out the law, by waiting out the statute of limitations," Schiff replied.
"So there ought to be a mechanism to make sure that that is not the case, whether that means revisiting the OLC opinion, and allowing the indictment of a sitting president and staying the prosecution, or allowing both the indictment and prosecution," he added.
Schiff said the DOJ might wait to see if Trump is reelected in 2020 before making any decisions.
Cohen on Wednesday was sentenced to three years in federal prison stemming from from eight federal charges he pleaded guilty to in August, including campaign finance violations tied to the scheme to pay off two women alleging affairs with Trump more than a decade ago.
Trump on Thursday tweeted that he "never directed Michael Cohen to break the law."