Luton have made their ninth summer signing following the arrival of winger Danny Green.
Notts County have signed Togo international Mawouna Amevor on a two-year deal.
The 21-year-old, who missed large parts of last season due to injury problems, has been linked with a move away from the San Siro after Milan failed to secure European football.
El Shaarawy enjoyed his finest season to date in 2012/13 as his 18 goals in all competitions alerted a host of European sides to his talents and helped establish himself as a regular for Italy.
Madrid were said to be among the clubs chasing the youngster, but his brother and agent, Manuel El Shaarawy, is certain that a departure will not happen.
"I read about an alleged interest from Real Madrid for El Shaarawy, but I can say without a doubt that Stephan will remain at Milan," he told Radio Kiss Kiss.
"He has a wonderful relationship with Pippo Inzaghi, who has always believed in him and his potential."