Carr left the Gunners out of his predicted final four, no doubt swayed by his many years with Tottenham Hotspur.
The former Republic of Ireland international spent a decade at White Hart Lane, making more than 270 appearances for the North London side and winning a League Cup.
Asked to predict his final four, Carr responded: "Leicester, Man City, Tottenham... Liverpool."
Quizzed over his Arsenal omission, Carr admitted: "It's more hope."
Arsenal are currently in third position in the Premier League table, eight points off leaders Leicester City.
Liverpool have climbed into seventh place after big wins over Manchester City and Crystal Palace, and are six points behind Arsenal.
If Arsenal fans are still believing they can catch leaders Leicester, then while Carr's comments may be biased, Liverpool have have to hope they can still go on and finish inside the top four rather than relying on the Europa League to qualify for next season's Champions League.