He said it could shift the "whole landscape of e-commerce" if it bought, for example, eBay.
He said it should ignore the wishes of activist investor Carl Icahn, who wants the company to buy back stock.
"Apple's about building great products, building and shaping markets," MrSculley said.
"Carl Icahn has suggested to [Apple chief executive] Tim Cook, 'Why don't you buy more stock back or make a bigger dividend?'
"I'd rather see Apple continue to invest in building... even make big acquisitions that were strategic, as opposed to buying more stock back, or giving more dividends."
MrSculley was the chief executive of Apple between 1983 and 1993.
During his tenure, he famously engineered the "forcing out" of Steve Jobs from the company - a decision he later said was due to his own inexperience in appreciating Mr Jobs' vision for future products.