Amorim will officially take charge of the 20-time English champions next week, with his first game at the helm set to be the trip to Ipswich Town on November 24.
According to Football Insider, Rashford will be 'on trial' for the remainder of the season, with Amorim wanting to have a good look at the forward before a decision is made on his future.
The report claims that the incoming head coach wants to see 'a significant improvement' from the England international, but if the attacker continues to struggle, then he could be sold during next summer's transfer window.
There has been much talk surrounding Rashford's suitability for Amorim's style of play, as the Portuguese uses a 3-4-3 formation at Sporting with two number 10s, which may be Bruno Fernandes and Alejandro Garnacho.
Man United 'could sell Rashford next summer'
Rashford is Man United's second-highest goalscorer this season with four, while he has also contributed three assists in his 16 appearances, but his overall performance level has again been below the standard that he set in 2022-23.
The forward managed 30 goals and 11 assists in 56 appearances during the 2022-23 season, which led to him signing a lucrative long-term contract with the 20-time English champions.
However, he found it difficult last term, managing just eight goals and six assists in 43 appearances, and there have also been off-the-field problems over the last year or so.
Rashford has another four years left to run on his contract at Old Trafford, but it is understood that a serious offer for him next summer would be considered, with Paris Saint-Germain still believed to have an interest.
PSG 'are known admirers' of Rashford
Last month, it was claimed that PSG were still keen on Rashford, with the French champions still searching for a replacement for Kylian Mbappe, who moved to Real Madrid over the summer.
Man United are believed to have previously placed a £100m value on their academy product, but PSG would not be prepared to go anywhere near that fee for Rashford next year.
Rashford is believed to have had a strained relationship with Erik ten Hag despite the former Man United head coach defending the attacker in public whenever he was criticised.
Amorim will now have to make up his own mind when it comes to the Englishman, and a change of manager at Old Trafford could potentially be the kickstart that Rashford needs to save his Man United career.