The US President surprised many by singing a couple of lines of 'Let's Stay Together' at a campaign fundraiser last week in tribute to Al Green, who was in attendance.
The 'Lost Without U' singer told TMZ that he is "always in support" of Obama and described his performance as "classic".
When asked if he would like to perform or write with the President, he added: "I'd duet with Barack any day."
Thicke and wife Paula Patton became parents last year to son Julian.
Watch Barack Obama sing 'Let's Stay Together' below: