He noted that Disney has received notable interest from many different entities in recent weeks.
A key decision looms for ESPN with the NBA, with those rights due to expire in 2025.
Ives sees ESPN as much more attractive to Apple than Disney overall.
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Its priciest deal to date has been the $3 billion acquisition of Beats in 2014.
The analyst noted the hawkish tone set recently by officials like Federal Trade Commission chair Lina Khan.
Cooks predecessor, Steve Jobs, was also a close associate of Igers.
