The defensive duo have both suffered with injuries of late, with Alexander-Arnold (knee) missing the last two games and Gomez (leg) the last 11.
Initially, the hope was that Gomez would return by the end of January, while Klopp was optimistic that Alexander-Arnold would be back ahead of schedule, but last week took a less positive approach.
Now speaking ahead of Monday’s clash at the London Stadium, the manager confirmed both would be unavailable, but said his No. 66 should be back in full training before the home clash against Bournemouth on February 9.
“[No] return date for Joe, and Trent is getting better and better and better,” he explained.
“[Trent is] really good. I hope he is in full training next week. That’s very good then, but not for now.”
A boost for this weekend is that James Milner returns from a one-match suspension to bolster the extended right-back ranks, with Klopp having fielded Jordan Henderson out of position for Wednesday’s 1-1 draw with Leicester.
“There was no doubt that we have internal solutions to different problems, so credit to the boys,” he said.
The vice-captain is likely to start at right-back against the Hammers, but Klopp was clearly pleased with Henderson’s contribution at Anfield.
More troubling is Gomez’s long-term absence, with the manager going on to cast doubt over his involvement for the Champions League last 16 clash with Bayern Munich this month.
“No, don’t think so. No,” he said when asked whether February 19 was a realistic return date.
“Yes, after that, any time—we will see.”
Otherwise he will need to be creative once again, for one of the biggest games of the season.