Kremlin spokesman Dmitry Peskov said neither Russia nor the pro-Russian separatists in eastern Ukraine who passed the sentence had heard from officials in London on the issue.
"You need to apply, of course, to the authorities of the country whose court passed the verdict, and that is not the Russian Federation," Peskov said.
"But, of course, everything will depend on appeals from London. And I am sure that the Russian side will be ready to listen."
The two Britons, Aiden Aslin and Sean Pinner, as well as Moroccan man named Brahim Saadoun, were sentenced to death last week for allegedly fighting as mercenaries by a court in the self-proclaimed Donetsk People's Republic.
The internationally unrecognised territory encompasses parts of Ukraine's eastern Donetsk region seized by Russia-backed separatists since 2014.
Both UK and Ukrainian authorities have declared the verdict null and void, with officials in London decrying proceedings as "a sham".
UK Foreign Secretary Liz Truss said earlier on Tuesday that the best route to secure Aslin's and Pinner's release was "through the Ukrainians" but added that she would do "whatever it takes".
Separatist authorities in Donetsk said the men had a month to appeal their sentences.
The Ukrainian government in Kyiv has since pledged to try to secure the release of all three through a prisoner swap with Russia.
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