The Japan international was stretchered off in the second half of last night's win at Sunderland.
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Endo was visibly upset as he was taken off at the Stadium of Light.
Slot said: "Yes, it's a serious one. How serious we don't know yet because it still has to be assessed tomorrow, but it doesn't look good.
"I'm not too sure (if it's his ankle). It's his foot, but if it is his ankle or his foot, that is what we have to assess tomorrow.
"I assume he will be out for a long, long time. What is long, it is difficult to say at this moment but you can hardly believe what this right full-back position brings us this season."