The veteran centre-back turns 35 next Monday and his existing deal only runs until June.
He made only his second Premier League start of the season in Saturday's 5-0 win over Norwich as manager Brendan Rodgers dropped Martin Skrtel, although he has played regularly in Europe.
It has been difficult for Carragher to watch from the bench for most of the season but he is determined to make the most of any opportunity.
Asked whether he could play on beyond this season, Carragher said: "That's up to the manager and the club will make decisions like that.
"I will just chat to the manager. I am open-minded and I am sure the club are as well.
"The most important thing is about the club getting results, not what I am going to do. That is something we can sort out one way or another."
Rodgers restored Carragher to the heart of his defence as he was concerned about the lack of leadership in the side after watching an insipid 45 minutes in the defeat by Manchester United.
The Reds boss has spoken of the significant contribution the defender has made during the early stages of his first season at Anfield having taken over from Kenny Dalglish in the summer.
"The manager has been great with me and has tried to keep me involved, even though it has been difficult for me to start games," added Carragher.
"I've played a lot in Europe, the FA Cup and Capital One Cup but the Premier League is the most important thing for the club and the players - we all want to play in that and I'm no different.
"The manager has always kept me involved, bringing me off the bench in different situations but I want to start.
"I am just pleased he gave me the nod against Norwich and it went well. I am just pleased I got a game and hopefully I can get a few more.
"That is only my second (league) start of the season, which is disappointing from my point of view but I won't complain.
"I will try to get as many more games as I can and try to stay involved from now to the end of the season."
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