Boateng ended a three-year spell in Serie A after agreeing a switch to Schalke last month, returning to the country of his birth to join Jens Keller's Champions League contender.
The 26-year-old left the field of play while representing Milan in a friendly at Pro Patria earlier this year after being subjected to racist abuse by a group of the regional club's supporters.
Schalke's financial chief Peters has insisted that Boateng considered racism as a factor in his decision to leave Milan, which was sealed after the Ghana international helped the Rossoneri secure Champions League qualification.
He told Bild: "Boateng wanted to leave because of the too many racist incidents in Italy.
"Milan President Silvio Berlusconi promised him that he would be able to go if Milan qualified for the Champions League group stages."
Boateng's bagged a brace in his last game for Milan, which helped Massimiliano Allegri's side negotiate a tricky Champions League qualifier against PSV Eindhoven.