Britain began air strikes in Syria this month as part of a US-led coalition targeting Islamic State jihadists while Russia has been bombing in the country since the end of September at the request of President Bashar al-Assad.
Russia has set up a system of hotlines with both the US and Israel to help avoid clashes in the crowded skies over Syria and the Russian statement said the British had now expressed interest in a similar arrangement.
There was no comment from the British defence ministry on the Russian statement.
The meeting came a day after President Vladimir Putin asked British Prime Minister David Cameron to get British experts to help analyse the black box of a warplane downed by Turkey as the two leaders discussed possible cooperation over Syria.
Britain has said it is considering the request from the Russian side and the Kremlin said Thursday that it was still waiting for a response.
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