It is unclear what or how severe the problem is but Gomez is understood to have sustained a fresh setback with Liverpool fearing the 23-year-old could be facing a lengthy spell on the sidelines.
England boss Gareth Southgate is due to hold his prematch news conference ahead of the friendly against the Republic of Ireland at 6.30 p.m. GMT and will provide an update on the situation then.
Any prolonged absence for Gomez would cause Jurgen Klopp a major headache given Virgil van Dijk is already in danger of missing the rest of the season having undergone surgery on a knee injury.
They were already expected to enter the transfer market after losing Van Dijk and opting not to replace Dejan Lovren, who was sold to Zenit St Petersburg in July, and a long lay-off for Gomez would only heighten the probability of making further signings.
Gomez was likely to play a prominent role in this month's England matches -- continuing with two Nations League clashes against Belgium and Iceland in the next seven days -- but his injury will likely increase Klopp's concerns that too much is being asked of players in a packed schedule.
"The Premier League has to change. Sky, BT, you -- everyone has to talk to each other," Klopp said after Liverpool's 1-1 draw at Manchester City last Sunday, speaking after Manchester United boss Ole Gunnar Solskjaer claimed his team had been "set up to fail" by being selected for the Saturday lunchtime game after playing in Turkey on the previous Thursday.
"You want good football? Give the boys a few hours more rest. These boys need rest. It's a difficult time. We want to play, obviously, but I heard Ole [Gunnar Solskjaer] yesterday as well and I understand him 100%. We are in the situation quite frequently.
"I spoke to the Premier League already and spoke to Pep [Guardiola] before the game about the five substitutions. Everyone watching is like: 'Oh, that's interesting.' But we have to change things and help the players. We want to play football, it's great. But playing Wednesday night and then 12:30 on Saturday is a crime and we have to change that."