The Hammers forward, who has been in scintillating form since the Premier League returned from lockdown last season, suffered a hamstring injury against Manchester City before the international break but has returned to training over the past two weeks.
While Moyes - who is confident Angelo Ogbonna will be fit after a groin problem - is hopeful Antonio can be involved, the 30-year-old will continue to be assessed ahead of Sunday's game at Bramall Lane.
"He's back doing quite a bit of training," said Moyes. "We've got a couple of days yet to see how he is. The truth is I couldn't give a complete answer but he is getting much closer, that is for sure.
"What he has done for us over the last few months, his form has been so good. He gives us a different outlet, he can run in behind or hold the ball up. He is a physical presence, his all-round play as a centre forward has improved greatly.
"If we can get him back that would be great, he is a really important player to the team and how we play and if we can get him back good, but I don't want to say if we can because we're not quite sure if he's ready yet."
Another hurdle for the Hammers ahead of the weekend was the return of international players. The Premier League are now testing players for Covid-19 upon their return from duty with their countries, and West Ham training on Friday was delayed in order to allow for results.
As of late on Friday morning, the east Londoners were still awaiting results to ensure everyone could train safely.
"The big problem is we're training this afternoon because we're waiting on all the testing to be confirmed from the international players and we've not had all the tests back, which is a bit disappointing," said Moyes.
"The testing is being done by the Premier League on all the international players who return and we've been guaranteed that all our players would get their test results back in time.
"We put training back today just to give us a bit of leeway and thank goodness I did, or we'd be hanging on to see who was training. Hopefully everybody will be fine but we don't have the results back yet."
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