"There is no doubt we will get reinforcements in January and there is no doubt that we will get the backing, but it will come down to two things - the availability and affordability of players," Rodgers told reporters.
The Anfield club are mired in mid-table with five wins from 17 Premier League matches, and were comprehensively outplayed in a 3-1 home defeat to Aston Villa on Saturday.
Luis Suarez and the injured Fabio Borini are the only recognised senior strikers after Andy Carroll was allowed to join West Ham United on loan in the last transfer window, while the club's efforts to bring in attack-minded players Clint Dempsey and Gylfi Sigurdsson were stymied, with both opting to join Tottenham Hotspur.
Suarez is single-handedly leading the attack, with usually consistent performers Steven Gerrard and Joe Allen looking tired.
Reports have linked Liverpool with Arsenal's Theo Walcott and Chelsea's Daniel Sturridge but Rodgers poured cold water on the suggestions.
"I see lots of names bandied about and, with all due respect, names that are pie in the sky because there won't be too many top players moving about in January because clubs want top money," he said.
"But there is no doubt that we want to bring in goals and we want to bring in players who can assist in scoring goals.
"If we can do that then that will set us up and then we can really reinforce again when the market opens up in the summer.
"All our problems were never going to be solved in this window because the January window is one of the least productive and the least movement goes on there but we will look to solve some of our problems in there and then we will look to revisit it in the summer." (Reporting by Josh Reich; Editing by Clare Fallon)