Everton boss David Moyes dispatched a scout to Croatia earlier this week with Mario Mandzukic understood to be the man on his radar.
The 23-year-old is currently playing for Dinamo Zagreb and is being tipped for a summer move to one of Europe's top leagues.
Mandzukic, who can play on the wing or up front, scored against England during the 4-1 defeat in the World Cup qualifier in Zagreb.
Werder Bremen have been long-term admirers, while Arsenal, Tottenham and Portsmouth were also said to be keeping tabs on him earlier this season.
Everton's spies made the trip to Croatia on Wednesday to see the cup clash between Dinamo and Hadjuk Split when Mandzukic played the 90 minutes during the 0-0 draw.