The 20-year-old scored 19 goals in 46 appearances in all competitions for the Serie A last term, proving potent in partnership with Mario Balotelli in the second half of the campaign.
It was therefore no surprise that top English clubs came calling for El Shaarawy but he turned them down, instead focusing on helping Milan improve on their third-placed league finish last term.
Milan vice-president Adriano Galliani said: "We received a huge offer for Stephan and he said the money he earns at Milan is enough for him.
"He's a fan of this club and he is more than happy here. I'm convinced he will play a great season."
Galliani was delighted with El Shaarawy's show of faith, given the current financial state of Italian football.
He believes it is "impossible" for someone like PSG striker Zlatan Ibrahimovic - who has played for both Milan and Inter, as well as Juventus - to return to Italy, while he also revealed that the club missed out on signing Dutch midfielder Kevin Strootman because he was too expensive.
Strootman subsequently moved to Serie A rivals Roma from Eredivisie outfit PSV for a fee in the region of €20 million.
"I think it is more than impossible for a player like Zlatan Ibrahimovic to return to Italy," he said.
"He has a salary which is not compatible with the Italian league."
On Strootman, he told Sky Sports Italia: "He's a really great player. We followed him for a year too, but he cost too much and we left. At this moment, €20 million is too much for Milan."