Sturridge signed a long term deal when he arrived from Chelsea 18 months ago but he has performed so well for the Reds that they are keen to agree a new contract with the 25-year-old England international.
Sturridge has scored 36 goals for Liverpool and his lethal strike partnership with the now-departed Luis Suarez was the key element in last season's Premier League title bid, which only just fell short.
Rodgers said: "There are talks ongoing with his representatives but there is no more news other than that."
Liverpool are hopeful Sturridge will be fit for the visit of West Brom on Saturday after a spell on the sidelines with a thigh injury, but he will sit out England's upcoming matches against San Marino and Estonia.
Rodgers said: "I have been in communication with Roy (Hodgson, England boss). We spoke at length yesterday on the situation. It was amicable, there was no issue.
"Every individual player you have to look at, every player is different. I respect that he has work to do internationally but my thoughts are with the Liverpool players and what their needs are.
"We agreed it was probably too soon for Daniel to meet up with England, irrespective of whether he was involved this weekend or not. He has not trained with the team at all since his injury and it probably was not the right time for him to go.
"He's had a grade one injury for four weeks, which is a long time, and my focus is now getting him to play for Liverpool."
Regarding Sturridge's possible availability for the weekend, Rodgers added: "We will have to wait and see."
Sturridge picked up the injury while playing for England and Rodgers complained subsequently that the player had not been given enough time to recover from the international.
Hodgson responded by saying that if players were given two days off after every game there would hardly be any training sessions.
Rodgers said: "I don't think the same thing will happen again. From the conversations with Roy, they will obviously look at that.
"I understand his position, where he has only a few days to work with the players. We work players here on the second day but it needs to be tapered to the individual player."
