Trump told reporters traveling with him on Air Force One that he may be able to make his decision on the Federal Bureau of Investigation head before he leaves in his first foreign trip later next week.
"Even that is possible," Trump said.
Critics have assailed Trump for abruptly dismissing Comey just as the agency is investigating alleged Russian meddling in the 2016 US election, and possible Moscow ties to the Trump presidential campaign. Russia denies the claims.
Trump said the candidates were "outstanding people" and "very well known."
The decision is subject to confirmation by the US Senate, where Republicans have a majority.
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