The Athletic says Amorim told Garnacho of his decision this week ahead of today's season finale against Aston Villa.
The Argentina winger is interesting Chelsea and former club Atletico Madrid.
Garnacho and his brother slammed Amorim after he was given barely 17 minutes as a second-half substitute in the Europa League final defeat to Tottenham.
His brother, Roberto, posted to social media in the aftermath: "Working as no-one else, helping every round, coming from two goals in the last two finals, just to be on the pitch for 19 mins and get thrown under the bus."
Meanwhile, Garnacho also stated after the Bilbao final: "Up until the final I played every round helping the team, and today I play 20 minutes, I don't know.
"The final will influence but the whole season, the situation of the club. I'm going to try to enjoy the summer and see what happens afterwards."