Matip has missed the last three games after suffering the injury at the end of November, with Klopp struggling for centre-back options in his absence.
Given the unpredictability of Lovren’s form, Matip’s persistent injury problems are a major concern, particularly given the failure to sign another defender last summer.
But while Matip was expected to miss the rest of the year while he recovers, Klopp is hopeful he can make an early return.
The 26-year-old is already back in light training, running outside while his team-mates prepare for Wednesday night’s Anfield clash with West Brom.
“It could be possible that Joel will be back for some of our Christmas games,” Klopp revealed.
“I really hope so but it’s not for sure at this stage. The fact he’s running again outside is a good sign. If nothing else happens then he will be close.”
Meanwhile Sturridge missed the Merseyside derby due to a tight hamstring, in another worrying setback having remained largely injury free for the last eight months.
The striker is likely to remain on the sidelines in midweek, but Klopp has stressed his problem is a “minor thing,” and could still feature.
“Daniel didn’t train, it’s only a very minor thing. We will see if he’s involved,” he said.
This could cast doubts over Sturridge’s future at Anfield, with both Real Betis and Valencia touted with an interest in a January deal.
It may be that, given his latest fitness worry, Klopp decides to cut his losses and allow Sturridge to leave in search of regular first-team football, with Solanke ready to perform.