Rodgers is interested in Basel forward Mohammed Salah but is not willing to pay the reported £16m price the Swiss club are asking.
Both the Northern Irishman and owners, Fenway Sports Group, are not against adding to the Reds squad to help push their hopes of returning to the Champions League next season, especially after the success of Daniel Sturridge, who arrived from Chelsea on January 2, 2013.
"There are no real developments yet," said Rodgers. "We have been working for a number of months on possibilities which can strengthen the team and we need to see how that goes over the next couple of weeks.
"I'm not concerned. The owners have been great in terms of if there is something there to be done that will help us then I am sure they will support that.
"I just think it is one where it will be a difficult market to improve on but it certainly won't be for a lack of trying.
"We are assessing a whole raft of players, it is just a question of whether they are going to be available to bring in now."
Rodgers is looking at getting summer signing Tiago Ilori some game-time on loan, however, although youngster Jordon Ibe seems less likely to be given the same opportunity despite the Liverpool boss suggesting last month he could also be loaned out.
"It is something we will look to do with young Tiago," he added of his 20-year-old £7million signing from Sporting Lisbon who has yet to make his debut and has featured in only three match day squads this season.
"He has come in and now knows what Liverpool is about and the standards required. It has been difficult for him in terms of game time because he hasn't played but he has come in and shown the profile of player we thought he would be.
"We will look to get him a loan period now. He needs to be playing."
Ibe, an arrival from Wycombe Wanderers academy at the end of 2011, has made only two appearances and Rodgers said: "Jordon Ibe is a boy who is in and around the squad so we are balancing him at the moment.
"He has been outstanding in training having been out for a few weeks with injury.
"He is a young player who is learning all the time and is in no rush to go out.
"At some point we will need to get him regular game time to push him forward as he can be a great player for us for the future."
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