The Kellogg appointed by President Donald Trump was interviewed by the TV company Fox News on Sunday after he returned from a trip to Ukraine.
I believe that both sides must give in a little. (Ukraine's President Volodymyr) Zelenskyj has already hinted that he can ease his stance on the issue of territories, said the former general Kellogg.
He then added that Russian President Vladimir Putin must also "soften his stance."
Zelenskyj has consistently held firm to a stance that territories taken by Russia and which Moscow demands to keep should not be part of a negotiation – a stance that the previous US government has backed.
Trump has previously said that he will put an end to the war, but has not clarified how much support Kyiv will receive from the US.