Both Moyes and Rooney have been at United's Carrington training complex over the last two days but Sky Sports understand that talks are still to take place between the two.
Rooney has been heavily linked with a move away from Old Trafford since former United boss Sir Alex Ferguson left him out of the starting line-up for a crucial Champions League match at home to Real Madrid in April.
Ferguson subsequently claimed the 27-year-old verbally requested a transfer but the player has yet to comment publicly on the speculation, amid reports he disputes Ferguson's version of events.
United - who insist Rooney is not for sale - are due to head to Thailand for the first leg of their tour of the Far East and Australia next week.
Moyes' first game in charge will come on 13 July, when United take on the Singha All Stars in front of a sell-out 48,000 crowd at the Rajamangala Stadium in Bangkok.
Despite there being no talks with Rooney, Moyes has been busy in his first two days in charge of United, appointing Ryan Giggs and Phil Neville to his coaching staff as preparations for the new season get underway.
It is also thought Moyes may also use his press conference to announce the signing of 22-year-old Barcelona midfielder Thiago Alcantara with a deal reportedly very close.
You can watch Moyes' first United press conference on Sky Sports News from 4pm.