By Howard Schneider

WASHINGTON (Reuters) - President Donald Trump signaled on Wednesday he could be moving closer to the mainstream on monetary policy, saying he had not ruled out reappointment of Janet Yellen to a new four-year term as Fed chair as he considers his choices for the central bank.

In an interview with the Wall Street Journal, Trump was asked if Yellen was "toast" when her term expires in February, a question that reflected a widespread assumption that he would put his own stamp on the monetary authority rather than rely on former President Barack Obama's choice to run the Fed.

Trump replied with his most explicit comments about the Fed since taking office, saying that Yellen was "not toast," that he had "respect" for her, and that he would prefer the Fed to keep interests rates low.

Though rates are rising under Yellen they remain low by historic standards. Yellen and other policymakers have emphasized that rates will rise only gradually in the months ahead, and that monetary policy would remain loose for perhaps years to come.

The Fed said it would not comment on Trump's remarks. Yellen, who like Trump turned 70 last summer, has said little about the subject other than that she intended to serve out her current four year term.

Trump will have a chance to appoint five of the seven members of the Fed's Washington-based Board of Governors, including a currently open job of vice-chair in charge of financial supervision.

His comments on Wednesday were cast in general terms. During the campaign he talked from both extremes - criticizing Yellen as a political hack who kept interest rates low to help the Obama administration, but also saying that as a businessman he liked to borrow cheap.

For President Trump, lower or slower-growing interest rates could make it easier to pay for any infrastructure program he proposes, and slow what has been a steady rise in the dollar that makes U.S. exports more expensive and hurts manufacturers.

In complimenting Yellen and citing the advantages of loose policy, Trump also appeared to downplay the likelihood he intends to reshape U.S. monetary policy along the lines called for by some of the more conservative voices in the Republican party.

Some key Republicans want the Fed to set monetary policy based on a mathematical rule. The most commonly used versions of those rules would recommend much higher rates for the U.S. at this point, with inflation near the Fed's target and the economy near full employment.

“Maybe he’s learning on the job,” said Carl Tannenbaum, chief economist at Chicago-based Northern Trust. While his statements as a candidate were aimed at the election, he is now in an administration being counseled by more orthodox voices sensitive to what is needed to keep global bond markets on an even keel, he said.

“It’s not easy to find somebody who is going to have credibility in that job," he said of Yellen and her possible replacement. "The confirmation process is not an assured thing these days. And the markets weigh in if they were to nominate somebody who didn’t share the Fed’s view of itself as independent.”

(Reporting by Howard Schneider; Additional reporting by Ann Saphir in San Francisco; Editing by Tomasz Janowski)