The forward, who has two goals in the last two games, has been one of West Ham's best players this season when fit and available but will enter the final year of his contract come the summer.
Despite four points from games against Chelsea and Newcastle moving the Hammers within touching distance of safety, Moyes does not want to take focus off their relegation battle.
"I think it is something that once we are in a position to look at it," said Moyes. "We can look at it but I don’t think it is something we are jumping all over just now. First of all we need to find out what league we are in, we have got a job to do.
"We have not taken our focus for one minute away from the next game. Maybe at the end of the season it will be something we will look at."
Antonio's goals have helped steer the Hammers back on course but, with four conceded across their last two games despite improved performances, Moyes doesn't want to have to rely on his forwards to dig them out of trouble every time.
West Ham host Burnley on Sunday night and the Scot has made it clear he expects better after sloppy mistakes cost them all three points on Tyneside.
"I said we can’t keep conceding goals and to be fair I don’t think prior to lockdown it was really what we were doing," said Moyes. "I think we were quite hard to beat and made it difficult.
"We’ve got to get back to that because if we’re having to score two every game it’s going to make it very difficult to get anything. They were made well aware after the game what I thought of them and what I thought was required. Don’t for a minute think that wasn’t passed on to them."