The newspaper reports that the Lions are interested in bringing in the Italian international as a replacement for star striker Burak Yilmaz who moved to China in January.
Liverpool have transfer listed Balotelli and want to offload him to free up the £80,000-a-week wages that he is currently on.
Galatasaray would however, struggle to match his current wages and will make an enquiry for a loan move.
The Istanbul giants are currently on a one-year UEFA European competition ban for breaching financial rulings.
The club will have to cut back on spending and either sell or reduce the wage packets of their highest earners such as Wesley Sneijder and Fernando Muslera.
Balotelli has just returned from a disappointing season long loan at AC Milan scoring just one league goal in 23 games.
The 25-year-old striker joined the Reds amid high expectations when he was signed for £16 million from Manchester City but he also failed to settle in at Liverpool.
Galatasaray won the Turkish Cup for the 17th time after beating Istanbul rivals Fenerbahce 1-0 at the Antalya Arena.