Jason Dodd may still have a future with Albion, despite being released.
The veteran defender has been invited back for pre-season training and could end up playing for the Seagulls again on a month-to-month basis.
Dodd is wanted by a couple of Conference clubs but the 35-year-old would prefer to stay in the League and is eager to make amends for an injury-wrecked year with Albion.
Dodd, signed on a free transfer last summer after 17 seasons with Southampton, was restricted to seven appearances by ankle and back problems as the Seagulls were relegated from the Championship.
"I want to go back down there to show what I can do," he said. "I feel I still have a bit of unfinished business.
"It was a disappointing season for me and I don't want it to end on a sour note with people thinking I just came down to muck about and for the money.
"That wasn't it at all. I could have gone elsewhere for more money but I had a chat with the gaffer, it was a challenge and that was what I wanted.
"I don't want to leave it with us going down and me only playing a few games. That's why Brighton get first port of call and if it doesn't happen then I will go down other avenues."
Dodd has backed Albion's decision to award new one-year deals to the long-serving quintet of Kerry Mayo, Gary Hart, Charlie Oatway, Richard Carpenter and Guy Butters.
"You need to keep them, if you didn't the club would be in freefall," he said. "Don't get me wrong, we all like to see exciting young players coming through, but they are not going to win you anything.
"You need three, four or five core players. They got the club out of League One before, so they know what is required. If you release them who are you going to get in?"
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