But the midfielder is available for the home first-leg clash with CSKA Moscow before another crucial encounter at the weekend against Chelsea in the Premier League.
Barry has only 18 months left of his current deal after a proposed £18 million move to Liverpool last summer never materialised.
But Agbonlahor believes it would send out a message of intent if the 28-year-old puts pen to paper on a new 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 admitted: "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."
Barry is hoping the Villa fans will help to create an atmosphere similar to when the midlands club gained a 2-1 win over Ajax earlier in the competition.
He said: "The atmosphere that night against Ajax was tremendous, one of the greatest I have known at Villa Park. It was a real night to remember.
"It felt like European football had well and truly returned to Villa Park and was fantastic. Scoring the winner in that game in front of the Holte End was one of the greatest moments of my career at Villa.
"We want to create a similar night to remember on Wednesday."
Barry is set to replace Steve Sidwell who will have to serve a one game ban for his sending-off against SV Hamburg in Germany in December.
Central defender Curtis Davies is battling to overcome the shoulder injury suffered during the 3-1 defeat at Goodison while striker Emile Heskey remains a doubt with the Achilles problem aggravated on England duty in Spain last week.
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