Liverpool manager Rafael Benitez hopes to persuade Daniel Agger and Dirk Kuyt to sign new long-term contracts with the club.
Both players still have 18 months left on their current Anfield deals but Benitez is keen to tie the duo to longer-term contracts.
The Reds boss said: "Agger is very close and he is talking with the club. 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."
Meanwhile, Kuyt is confident the Reds will bounce back from their surprise defeat at Tottenham by beating Atletico Madrid in the Champions League.
The in-form Netherlands international said: "Sometimes it is like this in football but we have come back from behind many times this season. We have now conceded late goals but we've had a really good season.
"As a team and as players, we don't look back too much. We just look forward and we can't wait to play the game against Atletico.
"We play in the toughest league in Europe so sometimes things like this happen and you just have to go on and play the football like we have this season, and I know we will win a lot of games in a row again."