Wayne Rooney has already held "serious talks" about ending his career in the United States, which could see him move across the Atlantic as early as next month.
However, the Mail adds that Moshiri agrees with Allardyce's decision to tell Rooney to consider finding another club as he can not guarantee him game-time next term - and that is a stance that has left many of Rooney's Everton teammates surprised.
Everton's manager next season could have a bearing on Wayne Rooney's future.
'There have been rumours about Wayne going overseas, China or America.
Wayne Rooney could be about to leave Everton for a second time.
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Allardyce revealed this week that he hopes the boyhood Evertonian will stay.
Wayne Rooney agreed to a deal to bolt Everton for Major League Soccer when the transfer window opens.
The 32-year-old returned to Everton this season after spending 13 years at Manchester United.
But heading to the US and to a team that really wants to feature him could work well for him.
Rooney has struggled at times with the pace of the Premier League and adapting his game to a deeper-lying midfield role which could make the lower standard of the MLS attractive.
DC United finished last in the Eastern Conference previous year, scoring a co-MLS-low 31 goals while surrendering 60, losing out on goal-difference to Western Conference doormat Los Angeles Galaxy for the league basement. England's all-time leading goalscorer wants clarity on Allardyce's position, or whether he features in the next manager's plans, before deciding whether to move with his young family to the US.