The 33-year-old central defender played every minute of the 1-0 play-off final win over Watford at Wembley, a match that went into extra-time and was settled by a Kevin Phillips penalty.
His contract expires at the end of this month and there have been outline talks about a new deal at Selhurst Park for the Wales international.
"I still think I have a lot to offer Palace," Gabbidon told the Sunday Mirror.
"We will have to see what happens in the next couple of weeks but, yes, I want to stay. I feel I can still play at the top level.
"I have a lot of experience and that has helped this season because we have a lot of young lads in the team.
"I have been able to give advice to the younger lads when they have needed it. That's my job. If I am not in the team, it is up to me to try to help them."
If Gabbidon is retained by Palace he could come up against former Selhurst Park team-mate Wilfried Zaha, who will begin next season as a Manchester United player.
Gabbidon feels the England international will only improve by being part of the Old Trafford surroundings.
He said: "He is an incredible talent. I have faced him in training and at times he is unplayable. He makes a fool out of you - and I hate marking him.
"Yes, he is still a bit raw but if he doesn't learn at United, there is no hope for him!"