The ex-Sunderland forward said that he is "excited" to see how the duo fare in their new roles, describing them as the "best" candidates for the job.
"It will be very exciting as they are two of the best in Irish football," The Express quotes Quinn as saying.
"It will be interesting to see as well how Roy will adapt to being a number two. They will need to kick on and build legacies."
O'Neill has signed an initial two-year contract as head coach, with former Manchester United midfielder Keane as his deputy.
The duo's first game in charge will be the friendly against Latvia on November 15.