In an interview aboard Air Force One on Friday Trump said that he had "better not say," when asked how many times the two leaders have spoken.
"He (Putin) wants to see people stop dying," Trump told the New York Post.
Kremlin spokesman Dmitry Peskov said on Sunday he could "neither confirm nor deny" reports of a conversation between Putin and Trump, Russian state news agency TASS reported.
In late January, Kremlin spokesperson Dmitry Peskov said that Putin is ready to hold a phone call with Trump, and Moscow is waiting for word from Washington that it is ready too.
On Friday, Trump said he would probably meet Ukrainian President Volodymyr Zelenskiy next week to discuss the end of the conflict.
The Russia-Ukraine conflict will mark its third anniversary on February 24.
Trump told the New York Post that he has "always had a good relationship with Putin" and that he has a concrete plan to end the conflict. But he did not disclose further details.
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