The Reds boss is hoping to draft in a new striker when the transfer window opens and Sturridge and Walcott have both been linked in the past but Rodgers is keen to play down the possibility.
Reports have suggested that talks have already taken place between Liverpool and Chelsea, while Sturridge's agents recently denied that the striker demanded £80,000 a week and regular football but Rodgers has refused to confirm that and has told fans not to expect too much in the new year.
"I see lots of names bandied about that are pie in the sky because there won't be too many top players moving in January as clubs want top money," he said.
"There is no doubt that we want to bring in goals and we want to bring in players who can assist in scoring goals. It is all about progress, and I believe we are making that, but you cannot solve all your problems in one leap."