This is the first interaction between them after Palaniswami assumed office in February 2017.
Patel took over as RBI chief last year.
"The meeting was a courtesy call", official sources said.
Patel was accompanied by RBI Regional Director (Tamil Nadu nd Puducherry), Arundhati Mech during the brief interaction.
Senior Tamil Nadu officials, including Chief Secretary Girijia Vaidyanathan and Finance Secretary K Shanmugam were also present.