Mourinho insisted on Friday that - in light of interest from Liverpool - Salah has agreed to join Chelsea, and Rodgers says there are other targets the club can now concentrate on.
"The young guy is a good player. We have tracked him for a number of months, the club has been watching him and I have been to watch him," Rodgers told talkSPORT. "It is one where the agent of the player and the clubs were talking but if the deal can't be done, the deal can't be done.
"He's a boy that is a talent. He is 21 years of age and people saw his qualities in the games against Chelsea and Tottenham in Europe. But you need to have that list [of targets] because if it doesn't work out then you are hoping there are one or two others."
Rodgers acknowledged that the January transfer window is a tough time to do business, but said that he is only interested in signing players who could make an immediate impact.
"I know the club has been working very hard to get players in. I'll leave that to them and see how they get on," he added. "January is a very difficult market. It is hard to bring in players that can improve the team.
"This is a brilliant club and we try to get players in for the now, we need players who can come in now and help us. I'd rather wait and look at our young players than bring in one or two squad players."