Speculation during the summer had heavily linked the striker with a move away from Old Trafford, with Chelsea known to have made at least two bids for his services.
However, Moyes, who took charge of United during the summer from Sir Alex Ferguson, insisted that the 28-year-old was not for sale at any price and he remained with the champions.
Since then, Rooney has produced a number of man-of-the-match performances, as well as scoring seven goals.
Reflecting on that form, former United defender Higginbotham told Sports Mole that both Rooney and his manager deserve the credit.
"He's been outstanding and he's been United's player of the season so far. He seems to have got that hunger back. There was a lot of talk over the summer and it really looked at one point that he would be leaving," said Higginbotham.
"You've got to give Rooney and David Moyes credit because whatever was said and done in the summer, it has worked to Manchester United's advantage. Rooney is playing as well as he has ever done for the club and Moyes has managed to get a top class footballer firing on all cylinders.
"He looks like the player of old and he wants to be in the thick of everything. There's no doubt that he has been United's standout player."
Rooney joined United as a teenager from Everton back in 2004.