Vance stated that it would not be "productive" for such a meeting to take place before the two leaders meet with US President Donald Trump, reports Fox News.
He added that the USA will continue an"open dialogue" with Ukraine and Zelensky.
Trump previously announced that he would meet with Putin in Alaska on August 15, but also that he was open to it being a trilateral meeting in which Zelensky would also participate.
Bloomberg reported that US and Russian officials are working to reach an agreement that would stop the war in Ukraine and would confirm Russian control over the territories Moscow has occupied since the beginning of the invasion.