Hamzaoğlu underlined that Galatasaray will try to sign Alves but that meeting his wage demands could be a problem.
“Dani Alves will come at a price but it is something we are interested in,” Hamzaoğlu told TRT.
“He is a great player and would boost the image of the club but we would not want to disrupt the squad harmony in the process.”
Galatasaray will have competition from Manchester United who are reported to be close to signing the Barcelona star.
The Daily Star claim that United have agreed a pre-contract arrangement deal with the Brazilian international but Barcelona are yet to confirm.
Galatasaray won the Süper Lig for the 20th time this season and became the first Turkish side to wear four stars on their shirt.
The Lions also won the Turkish Cup for the 16th time on Wednesday 3 June to win the double for the sixth time – a Turkish record.
Galatasaray will qualify directly for the Champions League group stages next season.