The meeting took place amid heightened activities among opposition parties ahead of the presidential election, to be held before July 24, when President Pranab Mukherjee completes his tenure.
The opposition parties are trying to have Patnaik's party, the BJD, on their side as it carries over 32,000 votes and can help them give the ruling NDA a tough fight in the poll.
"The two leaders discussed the possibility of fielding a consensual candidate by the opposition. Yechury stressed on fielding a person with secular credentials. Patnaik said the issue will be taken forward," CPI(M) sources said.
"Names of some probable candidates were discussed," one of the sources said.
The CPI(M) has already said like-minded opposition parties should work towards fielding a consensual candidate for the presidential election to ensure "secular supervision" of Rashtrapati Bhavan. It has termed the election, as the first "acid test" of the parties in their bid to halt the BJP's juggernaut.
Opposition leaders, including Congress president Sonia Gandhi, have held a series of meetings among themselves over the issue recently.