After leaving Atletico, Saul had held talks with Trabzonspor and was expected to sign with the Super Lig club.
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However, Saul has now pulled out of the move, explaining: "It didn't work out due to personal reasons. I hope our paths can cross again one day."
Saul spent last season on-loan with Sevilla, but he could now pursue his career in Brazil.
Transfer expert Fabrizio Romano is reporting Saul has received a three-year contract offer from Flamengo and is now leaning towards putting pen to paper.