That has inevitably led to speculation United may offer the 27-year-old a contract extension, something ex-manager Sir Alex Ferguson appeared to pave the way for with his conciliatory statements on Thursday – his first comments on the player since revealing he had asked to leave.
Moyes sidestepped that question at his press conference on Friday lunchtime, however, ahead of Sunday’s visit to Manchester City, the United boss confirmed he will carry on demanding more of the striker.
"I think we just go step by step," said Moyes.
"If he could score another two goals at the weekend that would be the next step forward wouldn’t it?
"He’s played really well and we want him to maintain that. If anything I’m asking him to step up again. I want him to keep getting better."
However, Rooney’s form has underlined the suggestion from the United camp at the start of pre-season that he had returned fitter than he had done for years.
"Wayne was in great shape just before he damaged his hamstring in Thailand," said Moyes. "I told you that but I don’t know if you all believed me.
"We thought (his hamstring) was going to be okay, but it wasn’t. We kept him working really hard and he was in really good shape.
"I was really impressed with the condition he was in and the work he did in pre-season. He is getting the fruits of that. He’s worked hard and is showing everyone exactly what he can do."