The Merseyside outfit have been tracking the 21-year-old for a "number of months", but it appears that Premier League rivals Chelsea are winning the race for his signature.
The West London outfit announced yesterday that they have agreed a deal with Basel for the Egypt international's services.
However, with the deal depending on the two parties agreeing personal terms, Rodgers has refused to give up hope of swooping for the player.
"I'm not sure whether that deal is definitely done yet or not," Rodgers told talkSPORT. "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.
"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. 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."
Reports have claimed that Chelsea made an offer of around £11m for Salah.