The 20-year-old scored 16 times for the Rossoneri before Christmas and although his record in front of goal dropped off after the January arrival of Mario Balotelli from Manchester City, he is still regarded as a great prospect.
El Shaarawy had said that while flattered by being linked with City, he was happy at Milan after reports emerged that the Premier League club have prepared a swap deal involving Argentinian striker Carlos Tevez for the left-footed forward, who joined Milan from Genoa in 2011.
Tuesday, Galliani confirmed he had not received an offer from City for El Shaarawy, however, on Wednesday he is quoted in Corriere dello Sport as saying El Shaarawy may not necessarily remain at the San Siro and pointed to Napoli as a possible destination.
He said: "El Shaarawy? We never said he is not for sale.
"Napoli? Ask the president Aurelio De Laurentiis."