The England striker missed United's midweek League Cup quarter-final win at Stoke City due to a groin injury but manager Moyes sounded slightly more optimistic after training on Friday.
"Wayne has got a chance," the Scot told reporters. "So we'll see how he is tomorrow."
The Premier League game at Old Trafford kicks off a busy period for the champions, who have last season's top scorer Robin van Persie sidelined by a thigh strain until January, with seven games in 21 days.
United are eighth overall, 10 points adrift of leaders Arsenal, but are on a bit of a roll after three wins in their last three games across all competitions.
Moyes said Portuguese winger Nani, who has not played since the home defeat to Newcastle United on Dec. 7, would be out for several weeks.
"Nani has a hamstring injury, which is a little bit worse than we thought," he said.
Ashley Young played against Stoke and scored his first goal in 18 months, becoming United's 14th different scorer in all competitions this season, and Moyes was pleased with the performance of some of those less in the limelight.
"The players have done really well," he said. "That is why there is such a good squad and a big squad here because throughout the season, the amount of games we have to play here, you do need those extra players.
"We have seen recently, in the last couple of games, we have been a little bit short in areas but the players who have come in have done brilliantly well. We have needed the whole squad, we really have."
The return of Scotland international Darren Fletcher, after almost a year out with a serious bowel condition, had also given everyone a lift.
"For Darren to get a couple of games and come back into the team is great," said Moyes
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