The technology group licenses its processing designs to Apple and receives a small royalty on every graphics chip used in a iPhone, iPad and Apple Watch.
Imagination, however, said it doubted that Apple could go it alone without violating Imagination' patents, intellectual property and confidential information.
"This evidence has been requested by Imagination but Apple has declined to provide it," it said on Monday.
It said that Apple's notification had triggered talks on alternative commercial arrangements for the current license and royalty agreement.
Apple paid Imagination license fees and royalties totalling 60.7 million pounds for the year to end-April 2016, half of its total revenue, and is expected to pay about 65 million pounds for this year, Imagination said.