Dmitry Peskov said the two leaders would not be able to meet “in a matter of weeks”, but added: “Let’s hope that it can happen in months to come.”
Mr Peskov confirmed negotiations between Moscow and Washington had yet to begin, but could get underway after the two world leaders manage to speak on the phone.
Mr Peskov said the two leaders would meet in months to come.
He said: “President Putin will call President Trump after the inauguration to congratulate him. It’s a protocol thing that has to be done.
“We expect that they may discuss their positions on a possible meeting.”
He added whenever the meeting happens, “Putin would be ready”.
Mr Putin has said he hopes for US-Russia relations to improve.
Mr Trump told the intelligence community the media had invented a "feud" between him and agencies.
Critics have expressed concerns over Mr Trump’s expressed admiration for the Russian leader over the course of his presidential campaign and since his victory in November – leading to accusations the new President had colluded with Moscow to win.
Mr Trump has said he would work with Mr Putin to tackle global issues including the battle against ISIS.
The Russian leader said he was hopeful relations could improve, but would bide his time while Mr Trump started to implement policy.
Donald Trump becomes 45th U.S. PRESIDENT
Fri, January 20, 2017
The inauguration of Donald Trump as the 45th President of the United States will mark the commencement of the four-year term of Donald Trump as President and Mike Pence as Vice President. A public ceremony will be held on Friday, January 20, 2017, on the West Front of the United States Capitol Building in Washington, D.C.
1 of 40
US President Donald Trump points to the stands as he walks with his wife Melania during the Inaugural Parade.
Get Quotes on Home Insurance
The confirmation comes after President Trump vehemently denied allegations of a vendetta with the American security services following revelations of Russian hacking in the US election.
In a speech to the intelligence community on Saturday, Mr Trump expressed admiration for the CIA’s work and blasted the media for inventing tensions between him and the agency.
He said: “Very, very few people could do the job you people do and I want you to know I am sop behind you.”
Mr Trump added: “I have a running war with the media. They are the most dishonest people on earth. They made it sound like I had a feud with the intelligence people.”