The report claims Boateng’s agent will enter negotiations with the Istanbul giants later today.
Schalke released midfielder Kevin-Prince Boateng after the 2-0 Bundesliga defeat by Cologne.
“Kevin-Prince Boateng and Sidney Sam have been released with immediate effect,” the club said in a statement.
Galatasaray would be able to sign the Ghana international as a free agent.
MLS side New York Red Bulls are also reported to be in the race for the Ghana intenational according to Gazzetta dello Sport.
The Lions are currently first in the Süper Lig, one point ahead of second placed Fenerbahçe and two ahead of third place Beşiktaş.
The Turkish giants are also competing in the Turkish Cup semi-finals and are expected to progress to the final after beating Sivasspor 4-1 in the first leg.
Galatasaray take on Mersin Idman Yurdu away from home next in the league.