The England international has been linked with a summer move away from Old Trafford, with Arsenal, Chelsea and Paris Saint-Germain all reportedly interested.
"I'm not surprised clubs like Chelsea and Arsenal want Wayne – he's a top player," The Mirror quotes Woodward as saying.
"He's not for sale and we won't be selling him. We are not looking to change the way we do things – it's been a successful formula.
"We want the manager to be investing. We are not in the business of delivering him players. That structure works for some, but not here at United. We backed Sir Alex Ferguson – we will do the same with David Moyes."
Moyes's first match as United boss ended in defeat as they were beaten 1-0 by Singha All Star's XI in Thailand.