Rashford has scored 138 goals in 426 appearances for the club since making his debut in 2016, having come up through United's youth ranks.
However, while he scored 30 goals in all competitions in the 2022-2023 season, he has struggled for form in three of the previous four seasons and attracted criticism from pundits and fans for a number of laborious displays during that period.
Amorim said he could “separate” the decisions of those advising Rashford from his relationship with the player.
“Right now I'm focusing on improving Marcos,” he added.
“We need a talented guy like Marcus. I forget about the interview now and see what I see on the pitch.”
Regarding Rashford's future, the Portuguese coach said that it is up to him and the club “to deal with that when the time comes.”
Speaking to the media ahead of their clash with Wolverhampton Wanderers on Thursday, Amorim denied that the talk about Rashford was just a distraction, adding: “Some players have a big responsibility here because they have been here for a long time.
“If you have great talent, (we need) great performance, great responsibility and great involvement to push everyone forward in this moment. Like any other player, (we want him to be) at his best.”
“This is probably one of the worst moments in our club. We have to face it and be strong.”
United's modest defeat to the Cherries means they head into Christmas in 13th place in the Premier League, after Wolves host Newcastle on December 30.
This would be their lowest position in the table at this stage since they were 15th in 1986, just over two months after Sir Alex Ferguson took over as manager.
Amorim had to stop his post-match press conference on Sunday due to a leak in the ceiling of the press room.
Asked later how he intended to turn around fortunes at Old Trafford, the former Sporting boss pointed to the ceiling and said: “If I knew, I would solve all the problems of this club, even this one.”
“I know what I will do. This is very clear to me. I will not say that I feel comfortable because I feel really frustrated. It is a very difficult moment but we will solve the problems step by step and find answers to everything.”