The 32-year-old scored on his debut for the Black Eagles in their 3-0 victory over Gaziantep in the Turkish Super Lig last week.
The Ghana international has joined the Turkish side on loan from Serie A outfit Fiorentina.
And the injury-prone former Schalke 04 forward has been told to play 9 matches to earn a permanent contract.
“If he plays 45 more minutes in 9 games, his contract will be extended. There will no rental," Besiktas manager Emre Kocadağ said.
"He played one, his contract will be extended if he plays 45 more minutes in 9 games. There will be no rental fee, we will only pay the full salary next season.
"There are 3 matches left to complete the mandatory option. We are still waiting for an answer for revision from the club. If these conditions persist, we will not pay. But we think his club would not want Rebocho to lose value by not playing .”
Boateng made 15 appearances for Fiorentina this season, scoring once.
His list of clubs include AC Milan, Tottenham and Borussia Dortmund, and played four times for Spanish giants Barcelona.
Although born in Germany, he made 15 appearances for Ghana while his half-brother - Bayern Munich defender Jerome Boateng - plays for Germany.