A move for Chelsea striker Daniel Sturridge is progressing after encountering a few hitches earlier in negotiations, with the player undergoing his medical on Monday.
The Reds are also hopeful of bringing former winger Tom Ince back to the club from Blackpool, but Rodgers stressed any new arrival would have to earn their place after rumours Sturridge wanted assurances he would get given a run in his preferred central striker role.
"No-one coming into this football club will demand where they play, that's for sure," Rodgers said.
"As with any negotiations between any club and any player it has not been straightforward.
"As you've seen over the last number of weeks, there are always going to be things written about players, clubs and dealings.
"Nothing will be complete until we've signed a player at the beginning of January but until anything is done on paper there is nothing to say.
"We'll always do our business privately and in the way we want to do it.
"We're confident we can get some business done early in January, which will really help the squad. Until that happens, there is nothing really to add.
"We don't want to make many [signings] in January, but the one or two we do I think can make a difference and help us. If we can do that, I think we'll have a good second half to the season."