Gomez, who has been a regular for the Reds, suffered the knee problem while on international duty with England.
Three Lions boss Gareth Southgate is expected to confirm the extent of the injury later though Liverpool are concerned Gomez could be out for a lengthy period.
Klopp is already without Virgil van Dijk for at least the majority of the rest of the season after the Dutchman suffered a cruciate knee ligament injury.
Gomez has been partnered by the likes of Fabinho, Nat Phillips, and Rhys Williams in Van Dijk’s absence.
Though Gomez’s injury will leave Matip as the only recognised senior centre-back in Liverpool’s squad.
Klopp has said the Reds will not buy in January but, depending on the severity of Gomez’s injury, he may now be left with little option.
Youngster Williams has played for the Premier League winning Reds this season.
And Klopp has said of his back-line: “Defending isn’t usually our problem because we do it as a unit.
“We didn’t say after Aston Villa [7-2 defeat] ‘Come on, we start again completely about how to defend.’
“We knew what we didn’t do right that night and maybe in one or two other games as well and we tried to sort that without overdoing it.
“But when you concede seven goals, it is not that you have to start at nil (the beginning) again.
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“We were quite relaxed about it, as relaxed as you can be in how we dealt with it. At the moment we lost, nobody was relaxed, we were all really frustrated about it but then how we responded, it was clear that it’s not all bad.
“We realised what was good before but some things needed to be adjusted.”