There was a doubt regarding whether the Reds' vice-captain would be available for the curtain-raiser at Anfield, after needing 15 stitches in his head following a sickening collision in a pre-season game against Napoli.
Despite the cut, Klopp spoke ahead of the clash against the Hammers and believes that the 32-year-old will play, joking that he may be sporting some additional headwear in order to do so.
As quoted by the Liverpool Echo, he said: "He should be okay. He is working with a headband, all of them different colours and all of them suit him! It is a pretty long cut. But it is Milly so he is not really bothered about it. Heading was never his best skill but we need his head from time to time, not only for heading."
Klopp however may not have a choice but to play the former England international on Sunday, as new summer signing Fabinho could miss the game due to injury, while the German would prefer to rest captain Jordan Henderson following his exploits for England at the World Cup.
Although there is a selection headache for the game, Klopp hopes he can call upon the former Manchester City man, who was a vital player for the Reds last season, featuring 42 times in all competitions.
He continued, stating: "We will figure it out. He said when the cut was open: ‘Don't think that this rules me out of next Sunday!' I don't decide that. It looks quite positive but I don't know yet 100%."