Carragher is second on the clubs all time record appearance list although he is currently unable to force his way into Kenny Dalglish’'s starting line-up. But his manager says his loyalty will be rewarded.
"We'll have the same conversations with 'Carra' to see what his plans and ambitions are and to see what he would like to do,” Dalglish told SkySports.
"We want to try and keep him involved at the football club for as long as we can.
Steven Gerrard recently signed a new five-year contract at Anfield, and in an era when few players stay at a club for their whole careers, Dalglish is aware that they deserve huge credit for their service.
"It's hugely important for us to keep people who have been great servants like Stevie and Carra have been.
"If they want to be here, we should do what we can to try to accommodate them.
"They are a fantastic asset to the football club both on and off the pitch, and that's something we should be looking to develop."