The Istanbul giants' trainer has revealed the winger is likely to leave to help alleviate the club's financial woes in the wake of their one-year European ban
The 28-year-old has been with the Portuguese national team as they reached the semi-final of Euro 2012, but is set to return to training on June 16.
Quaresma, along with compatriot Simao, have been transfer listed by the Istanbul club following the mounting financial crisis they face.
Besiktas are estimated to be in debt to the tune of €180-200 million. President Fikret Oman has made it the club's top priority to reduce the wage bill which means allowing their top earners to move on.
Now, coach Samet Aybaba has made it clear Quaresma is likely to leave, telling Lig TV: "The squad will be changed in the new season.
"I don't think Quaresma will be with us, because of his problems, because of what he has gone through.
"He's on leave until July 16. When he comes back, we'll see. We aim to play in a certain system and, of course, all of our players can be a part of this. When he arrives, we'll discuss this with him."
Both Simao and Quaresma are reportedly unhappy at the prospect of a season without European football, after UefA suspended Besiktas from European competitions due to the club's ongoing cash problems.
Rumours suggest Benfica could be interested in luring both Portugal internationals away from the Turkish outfit with the promise of Champions League football.
Quaresma has found himself at the centre of a number of controversies this season, the latest coming with his national side after he was filmed kicking out at his team-mate Miguel Lopes in training.
This comes after he was suspended by Besiktas after a half-time bust-up with former coach Carlos Carvalhal during the 3-1 Europa League defeat at the hands of eventual winners Atletico Madrid.