The England forward's temperament has often been called into question and he was arguably fortunate not to be dismissed in the early stages of Sunday's 2-2 draw with Cardiff City.
Jordon Mutch was the victim of a petulant kick from Rooney as the players tussled for possession, but the latter escaped with a yellow card.
Ahead of United's UEFA Champions League match at Bayer Leverkusen, Moyes told a press conference he was pleased to see Rooney demonstrating his hunger.
"It's a big part of his game. He's an aggressive player; he plays with his heart, as well as the skills he's got in abundance," said Moyes.
"That's the way he was when he was a boy at Everton with me.
"A lot of people said that might have been missing from his game last season - it's certainly not missing now.
"He's got the hunger back and the desire back and he's committed for everything. I'd rather have a Wayne Rooney that way than any other way."
Rooney has scored eight goals for United this season and his general level of performance has impressed Moyes.
"I want Wayne to have fire in his belly. I think he plays better when he's tough and aggressive," added the Scot.
"I don't want to change Wayne Rooney, that's for sure. I don't want him to be kicking at anybody, but I want him aggressive, challenging and full of running.
"And I think at the moment we're seeing a really good Wayne Rooney who's in top form and scoring goals as well."
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