Birmingham midfielder Charlee Adams has signed a new one-year contract with the club.
Southampton are confident Jay Rodriguez will commit to a new long-term deal but the player will consider his options.
United continue to be heavily linked with Cesc Fabregas and Marouane Fellaini, whilst it is also being suggested Newcastle's Yohan Cabaye could be of interest.
With Paul Scholes retired, Darren Fletcher's future open to debate and Anderson running out of last chances, it is easy to see why Moyes would be targeting that specific area of his squad.
Speaking to reporters in Sydney ahead of Saturday's 83,500 sell-out encounter with the A League All Stars, Moyes said: "When I got the job, I was made aware of what could possibly be done to improve things.
"Signing a midfield player was one area where we thought we could possibly add to the squad.
"It's hard to get top quality players who can come in and affect your team. That's why we're trying to go for what we see as the right players and the best players.
"If you're a player and you're brought up to play football, and you look out of the window and see Old Trafford, if you've got any ambitions about being a footballer, and you're a top-end one, then I think you'll want to play for Manchester United."
Robin van Persie was one who felt that way 12 months ago and was rewarded for the risk he took in leaving Arsenal by getting his hands on the Premier League medal he craved.
And now United hope Fabregas reaches the same conclusion after lodging a bid for the former Arsenal skipper earlier this week.
Not that Barcelona are giving them much encouragement.
Barca vice-president Josep Maria Bartomeu said: "Barca can assure everyone that they will not entertain any offers for Cesc.
"It is totally ruled out as Fabregas is non-transferable."
United do not see the situation in quite the same way, with Moyes admitting he was hopeful of hearing some news from executive vice-chairman Ed Woodward in the coming days.
"I couldn't tell you exactly," said Moyes, when asked for a progress update yesterday.
"I am in contact with the chief executive who has been dealing with it. I will hopefully know a little bit more in the next day or so."