Rooney has had long-standing issues with United and remains disenchanted at allegedly erroneous reports, fuelled by former manager Sir Alex Ferguson, that he made a formal transfer request.
The Mail on Sunday says Rooney and Moyes have been in regular contact and there have already been discussions on a personal level since Moyes returned to his desk last week.
"The two get on fine," said a source. "Wayne has trained with a lot of purpose and enthusiasm. He is clearly eager to get himself back in match condition."