Mannone enjoyed two loan spells at the KC Stadium last season and is keen to sever all ties with the Gunners this summer.
The 24-year-old was installed as the Tigers' first choice keeper and a move looked promising before Barmby left earlier this month.
"There was obviously more chance of me moving to Hull with Nick as manager but my agent is keeping in touch with the club," Mannone told the Hull Daily Mail.
"I have made it clear how much I have enjoyed my time with Hull. I love the fans and I love the club because they have given me such a great opportunity to play regular football.
"I feel as though I have been playing well this season and it would be a very good club to join but I still have a contract with Arsenal. It will be their decision too."