Rinaldi was part of the youth setup with Atalanta but had been spending this season on loan at Serie D side Legnano and it's been claimed that he fell ill last week.
The 19-year-old is said to have suffered the aneurysm while training at home and was quickly rushed to hospital in Varese, where he passed away on Friday.
"Andrea fought for three days after the illness that hit him," Legnano said in a statement. "An aneurysm snatched him out of life in the prime of his life, with a life ahead and with a career that promised bright goals. A sudden and shocking tragedy, impossible even to imagine."
The Italian midfielder who has been with this season's UEFA Champions League quarter-finalists since the age of 13, evoked an emotional message from the club.
"Always available and positive, he knew how to make himself well-liked by everyone," the club said. "Just as on the pitch you were always the last to surrender, this time too you fought with all your might not to fly away too soon.