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England s Gomez missed the start of the calendar year with a previous hamstring injury, and his return in this month s 1-0 FA Cup loss at Plymouth Argyle lasted only 11 minutes with the 27-year-old leaving the pitch after picking up a fresh knock, Reuters reported.
"Joe will take quite a long time. He s going to be out for numerous weeks because of a hamstring injury," Slot told reporters.
Slot said Gomez, a Liverpool player since 2015, may need surgery and would miss a large part of the rest of the season.
"We expect him to be back at the end phase of the season," the coach added.
"He worked really hard to come back. First game when he came back, after two or three minutes we saw him making a sprint, and now he s out for weeks again. That s always very hard for a player."
Striker Cody Gakpo, who missed Sunday s 2-1 win over Wolverhampton Wanderers with an injury, was close to recovery but remained unavailable for Wednesday, Slot added.
The Dutchman said Liverpool, who sit seven points above second-placed Arsenal, would face a difficult test at Villa, despite the ninth-placed side being winless in their last four league games.
"They qualified for top eight in the Champions League, so that tells you it s strong team we re going to face," he said.
"Again, a difficult game for us, for everyone. They have a great home record... that is going to be a challenge, but we have an okay away record as well this season."
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