Agger was sent off on Saturday as Liverpool suffered a crushing 3-0 defeat to West Bromwich Albion in their opening Premier League match.
Carragher believes that holding onto the centre-back pair is integral to Brendan Rodgers's hopes of a successful season in charge at Anfield.
He said: "It's probably not so good for me but, joking apart, it's absolutely vital we keep them.
"I know Vincent Kompany was great for Manchester City last season but, for me, as a defensive partnership these two are the best in the Premier League.
"I don't think either has signed a new contract just yet but Martin is very close and Daniel wants to stay at Liverpool. That's brilliant news."
Agger has been persistently linked with a move to reigning champions Manchester City, with Rodgers determined to keep the Danish international.