The Mail on Sunday says Rooney's situation will dominate David Moyes's first week of work - he officially starts at Old Trafford on Monday - with Arsenal ready to make a £20million bid for the striker and Chelsea also interested.
Rooney is said to be approaching the talks positively and is keen to start afresh with the new manager after his relationship with Sir Alex Ferguson soured last season.
He would prefer a move to Chelsea, but that is something United would be reluctant to sanction given they are likely to be title rivals next season.
French champions Paris Saint-Germain would meet United's £30m asking price, but Rooney is reluctant to move there with his young family.
Arsenal may provide a compromise, provided Rooney does not see it as a step down.