FIFA rules state that a player who refuses an international call-up cannot be selected for his club side.
But Liverpool said in a statement on Friday that all charges against the club and player had been dismissed by FIFA.
"Following FIFA's ruling, the club now considers the player available for selection," the Merseysiders added on their website (www.liverpoolfc.com).
Klopp had told reporters earlier on Friday: "It's difficult because there is not a lot of training time."
Liverpool asked for guidance on Matip's eligibility after a complaint was made to FIFA by Cameroon's soccer federation (FECAFOOT) concerning his call-up.
He was withdrawn from Liverpool's squad for the 1-1 Premier league draw at Manchester United last Sunday as the club sought clarity from FIFA on his eligibility and also missed Wednesday's 1-0 FA Cup third-round replay win at Plymouth Argyle.
Cameroon did not ask FIFA to stop Matip playing for Liverpool but they did not give permission for him to play either because it would have caused an outcry in the country with eight players having turned down call-ups for the finals.
Liverpool can cut Chelsea's lead at the top of the table to four points with a victory over bottom side Swansea City on Saturday as the pacesetters are not in action until Sunday.
Klopp is hopeful that defender Nathaniel Clyne and midfielder Jordan Henderson will also be available.
Clyne missed Liverpool's last two matches with a rib injury while Henderson sat out the FA Cup replay with Plymouth as a precaution after recovering from a heel injury.
(Reporting by Ken ferris; Additional reporting by Martyn Herman; Editing by Ed Osmond and Ken Ferris/Peter Rutherford)
