The Black Eagles have struggled at right back this season with Serdar Kurtulus being their only player who plays the position.
Besiktas failed to bring in a right back in the summer and have targeted Cicinho as a short term solution.
The 34-year-old right back has previously played for Real Madrid and Roma.
Cicinho has been in good form this season providing five assists in seven Super League appearances.
The attacking right back has two years remaining on his contract with Sivasspor.