Real Madrid coach Julen Lopetegui insists star midfielder Luka Modric will remain with the club this season.
Having featured for Croatia in the World Cup final in Russia, Kovacic wants a more prominent role in club football.
Chelsea may well be set to offer him an escape route.
The Croatia global has been yearning for a fresh challenge since his return from the World Cup and it appears that his wish could be granted before the transfer deadline.
Speaking after Madrid's 3-1 win over Juventus in the International Champions Cup on Saturday, Lopetegui pointed to Perez's statement as definitive.More news: Nikolas Cruz Bought Guns to Battle 'Demons' in His Head
Last month, Italy global striker Eder made such a move, swapping the Serie A club for Suning after two and a half seasons in Milan.
Thibaut Courtois is confident his refusal to return to Chelsea will be rewarded with a move to Real Madrid after the goalkeeper extended his absence into a second day.
Real Madrid is unable to provide him with the proper playing time to bloom so it will be best for both the team and the player to part their way.
Will Modric stay at Real Madrid this summer?
And, with Kovacic pinning his lack of World Cup minutes on his failure to nail down a starting spot, a new challenge in the Premier League now beckons. Have your say in the comments section below.