The technology company has offered Schiller and other key executives, including chief financial officer Peter Oppenheimer and operations director Jeff Williams, share options worth $60m (£37.4m) in the hope it will persuade them to stay at Apple for the next five years.
The reports come as the company looks to retain its leadership team in the wake of co-founder and former chief executive officer Steve Jobs’ death, who was regarded by many senior figures, including those outside Apple, as the brand’s driving force.
Current chief executive Tim Cook received a shares package reported to be equivalent to about $400m (£250m) when he took over from Steve Jobs earlier this year.
Apple said in a regulatory filing that its success depends on the “continued service and availability of key personnel”.
The statement also said: “Experienced personnel in the technology industry are in high demand and competition for their talents is intense, especially in the Silicon Valley, where most of the company’s key personnel are located.”
Apple missed its third quarter earnings expectations for the first time in three years last month as iPhone sales failed to reach analysts’ estimates. Profit still soared 54% in the quarter to a record high of $6.62bn (£4.2bn), on the back of a 39% jump in revenue to $28.27bn (£17.9bn).