Having initially wanted to see the Brazilian pushed out of Old Trafford, Amorim has been won over by the veteran.
Indeed, The Sun says the former Real Madrid midfielder could make United the final club of his career.
Amorim is convinced Casemiro's experience and leadership are a big asset and can play a major role in his plans to rebuild the team.
And confidants say Casemiro would welcome the chance to stay with United, despite bigger offers on the table from the Saudi Pro League.
Casemiro further confirmed his importance as he scored United's second goal in their 4-1 win over Athletic Bilbao in the Europa League semi-final on Thursday.