There is no rush for the Red Devils, with their in-form frontman having 18 months left to run on his current deal.
The England international's future at Old Trafford has been called into question on a regular basis in recent years and he was a target for Chelsea.
Rooney was reportedly looking for a way out of the club over the summer, having grown disillusioned with being played out of position, but he has returned to his talismanic best this term and appears to be enjoying his football again.
Taking that into account, Moyes is eager to avoid any potential distractions - with United playing catch-up in the defence of their Premier League title - and will shelve extension discussions until a more suitable time.
He said after seeing Rooney score a brace in Sunday's 2-2 draw with Tottenham Hotspur: "When will we talk to him about the contract? I don't really know.
"I think we are fine. We are just moving on from the summer. It will be done in good course.
"The appropriate people will talk when the time is right."
On Rooney's display against Spurs, which saw him draw United level on two occasions with an instinctive first-half finish and a second-half penalty, Moyes added: "Wayne has had a nice weekend. He is playing well and scoring - when the moment has come he has taken it.
"You will see him score a lot of great goals. But that (his first) was more of a sniff at goal, a mix-up in the box and he was on the end of it.
"His performances have been great and he's worked incredibly hard. And he deserves the rewards he is getting."
Two goals in the capital over the weekend took Rooney onto 164 in Premier League competition, placing him fifth on the all-time scoring list.
While he can take great pride from that achievement, he concedes that United have left themselves plenty of work to do in the pursuit of a 21st top-flight crown - with nine points separating them from table-topping Arsenal.
He said: "We didn't start the game too well. We gave away a sloppy goal on the edge of the box with the free-kick and made it difficult for ourselves.
"Thankfully, we got back into it and played some decent stuff. The lads did well, but then they hit us with the goal - it was a great strike by Sandro.
"We had to regroup and go again. We got the goal quite early on and I think 2-2 was a fair result.
"I'm confident and playing well but that's down to my team-mates.
"I'm just trying to do my job and help us to be successful. We're on a good run but need to try and turn some draws into wins.
"Spurs away is a difficult game but a point is probably a good result. It's the other games where we need to turn those points into three, that will make a massive difference."
@utd til I die - I doubt Ferguson would blantently lie to everyone for months and what I think happen from listening carefully and not getting carried away is that Rooney asked for a transfer but did not submit a written transfer request which is why he was able to deny asking to leave, and also Rooney had for more to lose from it getting out than Ferguson...- ray ray okocha