United, who face Tottenham at home on Wednesday evening, are only eight points behind leaders Arsenal and are on a six-game winning streak in all competitions.
Van Persie will not play on Wednesday, but is on the verge of a comeback and Moyes said: "We're definitely still in it. We're not breathing down the necks of the teams above us at the moment and we've got to try to get a wee bit closer, but once we get in that position people will know exactly what Manchester United are capable of.
"Robin is working with the medical people and when he is fit and ready he will improve us.
"We've still got a bit to catch up. We've a bit to do, so we've got to try to hang on to the others and keep winning. We've won six in a row now so we've got to try to keep our run going and keep progressing and keep as close to them as we can."
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball