The report from a Turkish newspaper 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.
Newcastle recently rejected a bid from Beşiktaş for Papiss Cisse according to the Express and Trabzonspor had also been closely linked with the Senegal international.
Cisse who has two years remaining on this contract joined Newcastle from SC Freiburg for €14.5 million back in January 2012.