The former Liverpool and Melbourne Victory winger was this week released from his short-term spell with Qatari club Al-Gharafa and Bridges says he will be speaking to his former Leeds United teammate about joining him in the Hunter Valley.
"Harry had a very good season with Melbourne Victory (in 2011-2012) and the Jets made their interest in him public before he signed for Al Gharafa," he told SBS.
"I'm going to be calling him again to see what his thoughts are. I speak to him once a week anyway and I know he's kept himself fit and would hit the ground running if he were to give the A-League another go.
"After being out of the game for a little while before going to the Middle East (nine months following his exit from Victory) I feel he also has a little bit of a point to prove to a few people and I think he'd be a great signing for the Jets and the A-League.
"As a player, he still has a huge amount to offer."