Russian Ambassador to London Andrei Kelin said on Tuesday that London had appealed to Moscow on the topic of the UK citizens and sent an "arrogant" note.
"This document is currently being considered in Moscow," Zakharova told reporters.
Earlier this month, the Donetsk People's Republic's Supreme Court announced death sentences for three mercenaries captured while fighting for the Ukrainian forces. Two of them - Aiden Aslin and Shaun Pinner - are UK citizens, while the third, named as Saadun Brahim, is Moroccan.
Russian and Donbass forces have repeatedly urged foreigners to stay out of the conflict in Ukraine, with Moscow warning that the rules of warfare do not apply to mercenaries, and stressing that anyone captured will be held criminally liable for their actions.