The Japanese striker is not first choice at Leicester anymore.
A move would appeal to him, as it would present a chance for regular first team football.
The offer from Galatasaray would come to £1.75 million, per Turkish outlet AMK.
A report in the paper suggests that Gala boss Fatih Terim wants Okazaki to play in the number 10 role just behind the striker in Turkey.
Okazaki was part of the club's title winning team a few years ago, but he has been reduced to substitute appearances in the Premier League this season.