The 20-year-old, who scored 16 goals in Serie A last season, has been hampered by injury at the start of the new campaign, which has restricted him to just five appearances so far.
El Shaarawy said that he enjoys a good relationship with strike partner Mario Balotelli, but it is the Brazilian who he cannot wait to link up with upon his return to fitness.
"My idol has always been Kaka, playing with him is a dream come true," the Italian international told Canale 5.
"I have a wonderful rapport with Balotelli. Last season, when things weren't going well, he helped me through tough times. He was a great support."
Kaka returned to the San Siro in the summer, four years after leaving for Real Madrid.