It cited Peskov as saying there had been no initial contacts between the two leaders about whether such a meeting was needed or where and how it might take place if it did happen.
Leonid Slutsky, head of the Russian parliament's international affairs committee, was cited by the state RIA news agency on Thursday as saying that preparations for such a meeting were at "an advanced stage" and that it could take place in February or March.
The Kremlin's Peskov said on Wednesday that contacts with Trump's team at the level of "individual departments" were intensifying, but declined to provide further details, Reuters reported.
Trump and Putin have both said they are keen to meet in person with the agenda, if such a meeting does take place, expected to focus on Trump's stated aim to bring a swift end to the Ukraine war.