According to the shoe giant's official website, the only way to get sponsored by Nike is if the company contacts you directly. Nike claims they "proactively seeks athletes to endorse the brand. Unsolicited Nike sponsorship requests are not accepted."
There are possibilities for Nike to not only accept, but grant donation requests. A detailed application available on Nike's website must be completed to ensure the request is reviewed. However, Nike clearly states they do not accept donation requests for money, only products. Nike is extremely protective over their brand because of their popularity. Because of this, they also choose to avoid targeting every athlete and school. They only target athletes and programs that represent a high standard of morals and social responsibility. From a profitable standpoint, they also search for athletes and programs that are marketable. To increase the chances for a sponsorship by Nike, become attractive from a marketable standpoint. Build a brand through social media, community and national networking and charitable services in efforts to have Nike to take a serious look at the brand. Nike is also committed to increasing their already popular international brand. Different countries have different cultures, so building a brand adhering to those specific guidelines could garner Nike's attention.