The Premier League star is said to have ended up in a casino with the X Factor group last December following the ITV show's final in Manchester.
"All the players were there and we ended up in the same casino," Josh told The Mirror. "I told Joe what a big fan I was and he said 'I love Union J'. I was just in awe thinking, 'this is England's number one goalkeeper.' We've had a bond since.
"Joe gave me some money to gamble with. I went to get my debit card to take out £50 and he withdrew like £100,000 and gave me some of his chips, they were worth £2,500. I was pretty drunk, but it was so cool."
Hart was dropped for City's last two fixtures following a number of goalkeeping errors, but the shot-stopper has been included in Roy Hodgson's England squad for the upcoming friendlies against Chile and Germany.