Donald Trump said he would "prefer" to keep his embattled deputy attorney general Rod Rosenstein - who oversees the Russia collusion probe - but that he might delay a politically risky decision on the official's fate originally expected for Thursday.

"I'd much prefer keeping Rod Rosenstein," Trump told journalists in New York on Wednesday.

However, Trump said that a meeting scheduled for Thursday at the White House between him and Rosenstein might be put off, because of the focus on a separate political drama over his Supreme Court pick Brett Kavanaugh.

"I may call Rod tonight or tomorrow and ask for a little bit of a delay to the meeting," Trump said.

No meeting with Rosenstein appeared on the president's schedule for Thursday, which was released by the White House.

Doubts over how long Rosenstein can keep the job have been swirling since shock US media reports that he once suggested secretly recording Trump to collect evidence for ousting him under a constitutional amendment for presidents unfit to remain in office.