The Scotsman will begin his six-year reign at Old Trafford this season following Sir Alex Ferguson's decision to retire after 26 years in charge.
"There is no doubt that he will bring in one or two players, but if I was a Manchester United fan I'd be more interested in seeing how he settles in as manager," the Irish Independent quotes Owen as saying.
"How he and his coaches settle is hugely important because they are the people who work with the players day-to-day. There is nothing wrong at Manchester United at the minute, it's just evolving really.
"I think everyone should be more conscious of David Moyes taking to it and his ideas being accepted. That's his main challenge."
Meanwhile, Sports Mole have compiled a list of five players United should sign.