Shaw made his return from a 10-month lay off in Amorim's first game in charge against Ipswich Town and has made another two appearances from the bench.
The 29-year-old was introduced as a substitute against Bodo/Glimt and Everton and he's now pushing to make his first start for United since picking up an injury on February 18.
Amorim discussed Shaw's eagerness to play when he was asked how long it would take to see a settled starting team in his new system at his post-match press conference.
"We want always two players [strikers] with different characteristics for changing the game but in the future, we'll have a structure or a base that is more clear in the team," said Amorim.
"We started this job now and now we have a lot of games. We are changing some details in training.
The load is different - I'm not saying better or worse, it's different.
"The way we play is different.
Sometimes we have more pressure and we have to make bigger distance running. We have a lot of players returning from injury. Kobbie Mainoo was a little risk because he was supposed to play just 60 minutes. Noussair [Mazraoui] clearly in difficulties.
"Luke Shaw wants to play more but we have to control it. So we have to rotate the team but, in the future, we will have a different system and you'll see more of a starting XI."
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