Kuyt and Agger have both just 18 months left on their current contracts.
“Agger is very close and he is talking with the club,” said Benitez.
“There is no news yet with Kuyt but he is another player that I would like to get done as soon as possible. They have to be done before the New Year.
“In each team you need people with quality, that work hard and with a good character.
“I want to do it as soon as possible because it is better for them and better for the club.”
The duo has been linked with moves away from Anfield in recent weeks, but Kuty has pledged to stay at the club.
“I’m really happy here and I want to stay, but so far there has been no talk of a new contract,” said Kuyt. “Hopefully that will come in the next few months.”
