The 19-year-old has signed fresh terms at the Keepmoat with his contract due to expire last month - one of only three players in the club’s U23s group to be offered a new deal.
Moore says the midfielder will be around the senior squad much more next season and believes he is fully capable of making the step up.
“I think we’ve got a nice little midfield player on our hands here,” Moore told the Free Press.
“I’m really pleased to get the deal done.
“He’s got the physicality to deal with it and the mentality too.
“I’m looking forward to working with him. He’s another youngster that we’ll get in the environment and he’ll come of age really quick.”
Greaves started two games for Rovers in the Leasing.com Trophy last season.
He has garnered attention as a combative midfielder but over the last 12 months has shown greater restraint and maturity on the pitch.
Moore is hoping to develop his ability on the ball but is confident there is plenty of quality there already.
He said: “AJ’s competitive, he’s a combative, different, no nonsense midfield player.
“He’s a ball-winner, he’s got great energy, he gets around and he’s tenacious.
“Also, in him and we’ll develop that side of his game, he sees a pass and he’s got a pass in his locker.
“We’ll develop that side of him, his ball skills and how he receives it.
“But what we can’t take away from him is his competitive style. We can control that a little bit and give a bit more to him.
“He played at Rotherham in the Leasing.com and he was tearing about that night and some of the experienced pros picked him off at times.
“That was a good learning experience for him.
“Stepping out of U23s, it’s different and they need to get that experience of the pace and it.
“That will have been a good experience for him.”