Anfield captain Steven Gerrard this week signed a new long-term contract at the club and accepted an offer to remain associated with the Merseysiders when he retires.
Dalglish would also like Carragher to eventually take up a similar position and discussions are set to take place with the centre-back.
Carragher, who is second in Liverpool's list of all-time appearances after 683 games, turns 34 at the end of January and has been out of the first team in the Premier League.
But Dalglish thinks the ex-England international is of identical importance to Gerrard, as the Reds boss said: "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.
"We want to try and keep him involved at the football club for as long as we can.
"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."
