The former Chelsea striker has been a revelation in a Reds shirt.
Rodgers told the Mirror: "I've known Daniel for a long time, since his early teens, so I've been able to follow his progress closely.
"There had been talk for some time about Daniel coming to the club but we needed to be sure that he was going to be the right fit for what we required.
"He has settled in very well, but he still has lots of aspects of his game to work on in order to achieve what he wants to and to allow him to make the kind of impact that we want. He has made a very promising start and as long as he maintains that same level of commitment and responsible attitude to improving, I can see him being a great signing for the club."