The Spaniard, who moved to Old Trafford from Athletic Bilbao in the summer, has not played since United's opening-day 2-1 defeat to Swansea City in August.
The 25-year-old suffered an ankle injury in training, but could be in contention to feature in Louis van Gaal's team at Old Trafford this weekend.
The midfielder wrote on Twitter: "Training hard and looking forward to this next game at Old Trafford!"
Training hard and looking forward to this next game at Old Trafford! pic.twitter.com/uQMwGK0kc6— Ander Herrera (@AnderHerrera) September 8, 2014