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Rashford has scored 138 goals in 426 appearances for the club since making his debut in 2016, having come through the United youth ranks.
However, while he managed 30 goals in all competitions in 2022-23, he has struggled for form in three of the previous four seasons and attracted criticism from pundits and fans for a number of laboured displays during that time.
Amorim said he can “separate” the decisions of those advising Rashford from his relationship with the player.
“At the moment I’m focused on improving Marcus,” he added.
“We need a talented guy like Marcus. I forget the interview now and see what I see on the pitch.”
Regarding Rashford’s future, the Portuguese boss said it is for him and the club “to deal with that when the time comes”.
United’s humbling defeat by the Cherries means they head into Christmas in 13th place in the Premier League.
It will be their lowest position in the table at this stage since they were 15th in 1986, just over two months into Sir Alex Ferguson’s reign as manager.
Amorim’s side face Wolves at Molineux on 26 December before hosting Newcastle on 30 December.
