Milan are working on an agreement with Besiktas, but Junior Messias reportedly remains determined to reject a move to Turkey.
The Rossoneri had hoped to push the Brazilian out of the squad to save on his salary and make room for the new arrivals.
According to Calciomercato.com, they are close to working out terms with Besiktas for them to take Messias on loan with an option to buy at the end of the season.
However, Messias is still not happy with the idea of leaving Italy and will say no to the Besiktas move, regardless of the personal terms on offer.
The 32-year-old has a contract that runs to June 2024 and was signed from Crotone for a total of €7.5m.
He has been in Italy since 2011 and worked various menial jobs including delivering refrigerators while also playing football on the side for lower league sides.
He only made his Serie C debut in 2018 and joined the professional leagues, shooting to fame in Serie A with Crotone in 2020.