The 25-year-old is widely expected to leave Anfield in the coming weeks in search of first-team football, and has been touted as a target for the Scottish champions.
Celtic have already brought in French youngster Odsonne Edouard on a permanent basis during the off-season for a club-record fee, however, and Rodgers will now focus on bolstering other areas of the field.
"Danny is a fantastic player and has been really, really unfortunate for a few years with injury but I have got the three strikers at the moment and we don't need any more," he told reporters. "We just signed young Odsonne Edouard on a permanent deal and he is a class act. We also have Moussa Dembele and Leigh Griffiths so with those three we are well covered.
"We were very keen to make the move permanent, he's a real class act, how he moves, the goals he gets, and his football intelligence. It's a great move by the club to sign him on a permanent deal. This boy has still got a lot of improvement and learning to do but he's a fantastic young talent.
"We know we need to strengthen. We lost Stuart Armstrong and Patrick Roberts, who were really influential players for us in all the years I have been here. We need to at least replace that and if we can also add to the squad. There is always speculation and rumour around players coming here or players leaving the club. You just have to stay concentrated, that will be a club decision in the end whatever happens."
Armstrong joined Southampton for a fee of £7m earlier this week, while Roberts returned to parent club Manchester City following a loan spell at Celtic Park.