However, when asked a corresponding question later in the day, NATO Secretary-General Jens Stoltenberg stated that it was necessary to engage with the Kremlin.
"To meet President Putin is not in any way contradicting NATO policies, because NATO is in favor of dialogue with Russia. And if you want dialogue, you have to speak to the political leaders. Several NATO leaders have met President Putin," he told journalists after his speech in London.
The NATO chief went on saying hat meetings between officials from Russia and the alliance had taken place as part of the NATO-Russia Council (NRC). Stoltenberg further underlined that he had previously met with Russian Foreign Minister Sergey Lavrov.
"The whole message of NATO is that we don’t want a new cold war, we don’t want a new arms race … We want to talk to Russia," Stoltenberg emphasized, noting that a dialogue with Moscow fell within NATO's interests.
The British government fears that the two presidents could meet before NATO's upcoming summit in Brussels and Trump's official visit to London.
"It's unclear if this meeting is after or before the NATO and UK visit. Obviously after would be better for us," the Times quoted a Whitehall source as saying.
"It adds another dynamic to an already colorful week," the official added.
The Times also quoted a Western diplomatic source as saying that if Trump and Putin meet before the July 11 NATO summit in Brussels, this would be viewed as a highly negative development.
On Friday, Donald Trump told reporters that it was possible that he would meet Vladimir Putin this summer.
Trump, who had two meetings with Putin during last year’s G20 summit in Germany, has shown a keen interest in restoring Russia’s place in the international community.
At the G7 summit in Quebec earlier this month, he proposed that Russia should be re-admitted to the Group of Eight countries.