United acted quickly after Sir Alex Ferguson's retirement was confirmed on Wednesday. Reports said Moyes has already informed Everton of his decision to leave them when his contract expires on June 30.
Rooney was sold by Moyes to United for 27 million pounds (32 million dollars) in August 2004.
A United spokesperson said late Wednesday Rooney was "not for sale," but the identity of Ferguson's successor will encourage potential suitors, according to media reports.
There has been speculation about the England forward's future since he was left out of the Champions League last-16 tie against Real Madrid.
Reports said Rooney asked Ferguson two weeks ago for a transfer, although after that informal request was rejected, he has not filed anything official.//DPA