Trump's call for a ceasefire on Sunday came as news to Ukrainian President Volodymyr Zelenskyy.
But if the Russians agree to an energy ceasefire, Ukraine will do the same, he told Axios.
Russia has not confirmed that any agreement has been reached with Ukraine.
"The talks are continuing. When we have something to say on the issue, we will of course let you know," Kremlin spokesman Dmitry Peskov told AFP on Monday.
After Trump's remarks on Sunday, several energy facilities in Ukraine have been attacked.