Vladimir Putin is turning to North Korea to replenish the arms supplies that have been run down by the conflict in Ukraine, US officials believe.
Pyongyang appears ready to provide weapons to Russia in support of Moscow's invasion.
North Korean leader Kim Jong Un was reported to have set off for Russia in his armoured train on Sunday night.
A possible venue for the meeting is the eastern Russian city of Vladivostok, where Mr Putin is attending an international forum.
Downing Street said like-minded democratic allies were standing together against Russia, while Mr Putin was attempting to secure arms from other authoritarian states.
"First and foremost, it is obviously right for democratic countries to seek to further align and deepen partnerships in the interests of peace and stability," the Prime Minister's spokesman said.
"That is very different from an approach that appears to be largely based on the selling of arms to support an illegal war. I think it's important to draw a distinction between the two."
Meanwhile, the Government said a message of "good wishes" sent from King Charles on North Korea's national day was intended for the people of the country, not the regime.
The King's message was sent via its embassy in London.
It read: "As the people of the Democratic People's Republic of Korea celebrate their national day, I send my good wishes for the future."
The King's message would have been sent on advice from the Foreign Office, and similar greetings were issued by his mother, the late Queen Elizabeth II.
The 75th anniversary of North Korea's founding was marked with a parade in Pyongyang on Saturday.
In Westminster, the Prime Minister's official spokesman played down the significance of the message.
"My understanding is this was a message to the people of North Korea rather than the regime," the spokesman said.
"I think this is something that happens each year and is not unusual in that regard."