The Red Devils, who appointed Moyes as Sir Alex Ferguson’s successor in the summer, are eight points behind leaders Arsenal after a run of four successive top-flight victories.
We’ve got to try to get a wee bit closer
The defending Premier League champions face Tottenham Hotspur on New Year’s Day, and Moyes is optimistic about their chances of retaining the English crown.
“We’re definitely in it,” Moyes said.
“But we’ve got a long way to catch up. We’re not breathing down the necks of the teams above us at the moment. We’ve got to try to get a wee bit closer because, once we get in that position, people will know exactly what Manchester United are capable of.
“Right from the start I said it was going to be an unpredictable season, with so many changes at the top clubs. Probably the stability at Arsenal has given them that continuity that has allowed them to start the season well.
“But I’ve not changed my opinion – I still think it looks like it’s an interesting season.”
MORE: Latest Man Utd news
MORE: Latest Arsenal news
MORE: The latest football news