The meeting between Mr Rao, who heads Telangana's ruling party TRS, and Mr Patnaik, the BJD chief, would take place in Bhubaneshwar.
Owing to the Odisha assembly currently being in session, it has been decided to hold consultations in next month, the release said.
In his bid to cobble together a front of like-minded non-BJP and non-Congress parties, Mr Rao had met West Bengal Chief Minister Mamata Banerjee in Kolkata last month. He had also held consultations with former prime minister and JD(S) boss H D Deve Gowda as per his plans to forge an alternative front.
On her part, Ms Banerjee had held consultations with NCP leader Sharad Pawar and Sanjay Raut, a Rajya Sabha MP of the BJP's estranged ally Shiv Sena, to discuss ways to forge an anti-BJP front at the national level.