Skipper Ledley suffered a slight groin strain that forced him off against Birmingham City on Boxing Day and out of the rest of the festive period.
Edgar missed the games at Manchester City and Leicester City with an ankle problem while Young-Pyo picked up a knee injury at the City of Manchester Stadium last week.
Teemu Tainio, who returned as a substitute at Leicester after illness and Andy Reid, who damaged knee ligaments at Middlesbrough in December, are also available.
It means Head Coach Martin Jol has a full squad to choose from for Anfield with the exception of Noureddine Naybet, who is with Morocco for the African Nations Cup.
"Everyone is back in training so we'll make an assessment and then pick the squad for Liverpool," reported Martin.
"They are all back and they look fine. Ledley hasn't played for a couple weeks so hopefully he will be 100 per cent but both Edgar and Lee are fine."
Ledley King, Edgar Davids and Lee Young-Pyo are all training again and back in the frame for Saturday's huge clash at Liverpool.