The group calling itself Community of Officers for International Security, which is based in the Central African Republic, published its offer in a letter.
It is not clear if it has been or will be accepted.
Burkina Faso is now led by a military junta that overthrew the government of President Roch Kaboré on Monday.
The letter, which has been verified by a Russian security adviser to the CAR presidency, also takes a swipe at the French-led offensive against extremists in the Sahel.
