Barry has only 18 months left on his current deal.
Agbonlahor said: “I think Gareth ought to sign a new contract. It would show our expectations for the rest of the season and next season.
“I don’t really like commenting on him but it would mean a lot, especially for the young lads because he’s been here so long.
“I’d like him to stay at the club but obviously it’s his choice what he does. If he stays and Stiliyan Petrov signs his new contract, it will be good for the club.
“Gareth is really good with the whole team and that’s why it’s been good that he’s been captain because he sets a good example.”
Agbonlahor continued: “I used to watch him a lot when I was coming through the ranks here. He’s been at Villa a long time and he hasn’t missed many games either.
“He does seem like an old man to me! But he doesn’t look it, he looks young, and he doesn’t play like it.”