"We seek to access reserves in Nigeria and produce them. Our focus is 2.5 million barrels and 4 million barrels potential of proven reserves," Tinubu said.
He added that the Lagos-based company was interested in acquiring some of Shell's onshore blocks in the Niger Delta.
Shell has so far sold three of its 30 onshore licenses and a fourth deal is about to be sealed.
Nigeria is drafting a new petroleum industry bill that Oando expects will force large oil companies to sell several billion barrels of oil reserves they don't use, Tinubu said.
Oando, listed on exchanges in Nigeria and South Africa, said in April it plans to raise $500 million in a share sale and list its stock in London to fund expansion.
