The young striker's superb form in Serie A has seen him linked with moves to Manchester United and Manchester City.
The 20-year-old has scored 14 times in domestic and European competition so far this season and Milan are keen that he should sign a new contract to keep him at the San Siro.
El Shaarawy scored his first senior international goal against France in November, leading Galliani to sing his praises.
"El Shaarawy is going beyond our expectations," Galliani declared.
"He only turned 20 a couple of weeks ago and I don't know if many other attackers his age are scoring with his continuity.
"He is one of the best players in the world, he is like Neymar. He's a serious and mature player."