WASHINGTON (Reuters) - U.S. Senate Majority Leader Mitch McConnell on Tuesday raised the possibility of a spirited battle over how an impeachment trial for President Donald Trump would be run and suggested that the referee - Supreme Court Justice John Roberts - not meddle.

Under the U.S. Constitution, if there is an impeachment trial for Trump, Roberts would preside over it.

“I would anticipate the chief justice would play a passive role” much like then-Supreme Court Chief Justice William Rehnquist during the impeachment trial of President Bill Clinton in 1999, McConnell told reporters in the Capitol.

Rehnquist was seen as giving senators latitude in deciding the shape of Clinton’s trial.

The U.S. House of Representatives is investigating Trump over his attempt to pressure Ukraine into investigating Democratic former Vice President Joe Biden, a political opponent of Trump.

Democrats, who control the House, are on the verge of writing and passing articles of impeachment against Trump, which would trigger a trial in the Republican-led Senate. A guilty verdict - seen as a long shot - would oust Trump from the presidency.

McConnell was asked by reporters how he would craft trial procedures that could determine the length of the procedure, the handling of witnesses and whether senators could pose questions.

McConnell said it was too early to know how everything would run. He outlined options for deciding, such as a bipartisan deal brokered by him and Senate Democratic Leader Chuck Schumer. Alternatively, McConnell said, a coalition of 51 senators -- a simple majority of the Senate -- could strike a deal on rules.

If both efforts failed, McConnell said, the trial could begin with the basics that everyone could agree upon: House Democrats presenting their case followed by a rebuttal from Trump’s lawyers.

Then, a floor battle could be waged over next steps.

McConnell said a series of proposals could be put up for a vote, if Roberts allowed such a game plan, to see which one could win enough backing for approval.

As during Clinton’s trial, one such proposal could be to dismiss the case with a simple majority vote.

Republicans hold 53 Senate seats, while Democrats control 47 when counting two independents who often align with them.

Schumer told reporters he hoped for a bipartisan deal with a “full” and “open” trial that is not cut short.

While McConnell has been deflecting reporters’ questions about a trial, it clearly is on his mind. He said he recently brushed up on the subject “by reading a little book” called “Impeachment: An American History.”