Antonio moved level with former Hammers favourite Paolo Di Canio on 47 goals with his strike in last weekend's 4-2 win at Newcastle.
Boss Moyes is hoping the powerhouse winger-turned-striker can go out in front on his own by finding the net against Leicester on Monday night.
“He's joint top now and because of that I am sure Micky will break the record," said Moyes.
“If it happens this Monday night it would be great but if it is not this Monday I am sure it will be in the near future.
“I think Mick will see it as a big deal and so he should do because West Ham, if you look through the eras, have had so many great players.
“So I think that for Micky to have the chance to do it, having started as a winger and then full-back and wing-back, for this period in his career he is a centre-forward so I hope he gets in front by about 20 or 30 goals ahead of Paolo Di Canio. I hope he makes it very difficult for anyone to catch him."
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