News channels and websites reported Hagi, a former midfielder for the club and one of Romania's greatest ever players, was sacked on Tuesday but Galatasaray had previously declined to comment.
Hagi, 46, had succeeded Frank Rijkaard as coach in October.
One of Turkey's most decorated teams suffered nine defeats in 18 official games since his appointment and they lie 11th in the 18-team Turkish Super League, 27 points behind leaders and Istanbul rivals Fenerbahce.
In Hagi's last game in charge, Galatasaray lost 2-1 at home to Fenerbahce a week ago.
Galatasaray were also eliminated in the quarter-finals of the main Turkish Cup competition earlier this month.
During an illustrious career, Hagi won 125 international caps and played in three World Cups - 1990, 1994 and 1998.
At club level he helped Steaua Bucharest to the final of the 1989 European Cup, enjoyed spells with Real Madrid and Barcelona and had a key role in the Galatasaray team which won a string of league titles and the UEFA Cup in 2000.
Nicknamed "The King," Hagi won Romania's all-time greatest player award in 2000 but has had a chequered career as a coach, with short spells at a series of clubs in Turkey and Romania.
Hagi previously coached Galatasaray in 2004-2005, when he led them to victory in the Turkish Cup. He resigned at the end of that season, when they finished third, complaining about a lack of support from the club's directors.
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