France has 400 special forces stationed in the country to battle a jihadist insurgency.
But relations have deteriorated in recent months, and Burkinabe Prime Minister Apollinaire Kyelem de Tembela in November said he hoped to "diversify partnership relations" in the fight against jihadists.
That "diversity" may include Russian forces, or possibly, mercenaries such as the Moscow-back "Wagner Group."
Burkina Faso, once a French colony, now seems to be moving down the same path as nearly Mali, after officers seized power there in September, in the second coup in eight months.
"Russia is a reasonable choice," Tembela said on Saturday after meeting Russian ambassador Alexey Saltykov.
The premier also made a discreet visit to Moscow in early December.