Storchak sent a proposal to Greek Prime Minister Alexis Tsipras earlier in the week to become a member of the bank.
When asked whether Greece's ascension into the bank would be discussed before the BRICS summit in July, Storchak said, "No."
"In accordance with the charter, the new [BRICS] development bank is open to any sovereign member of the United Nations Organization," Storchak added.
The BRICS New Development Bank was created in mid-2014 by an agreement between Russia, Brazil, India, China and South Africa. The member states also agreed to establish a $100-billion liquidity reserve to maintain the bank's financial stability.
The bank was designed as an alternative to Western global financial institutions.