The report claims that the Lions made an enquiry for the Senegal international and that Newcastle are prepared to listed to offers.
Galatasaray are in the transfer market for an additional striker and were closely linked with Zlatan Ibrahimovic last month.
The Lions won the league title for a record 20th time last season and earned the right to wear a fourth star on their crest. The Istanbul giants will play Champions League group stage football for the fourth consecutive season.
Cisse who has two years remaining on this contract joined Newcastle from SC Freiburg for €14.5 million back in January 2012.
The experienced striker is keen on staying at Newcastle over the summer and scored 11 goals in 22 appearances for the Premier League outfit last season.