The Toffees are interested in the 19-year-old, whom manager Ronald Koeman got to see first hand in their recent Europa League qualifier, and on Monday Hajduk club president Ivan Kos admitted they could sell their prize asset before Thursday's deadline.
In a tweet the Croatia Football Federation confirmed Vlasic had on Tuesday asked permission to leave the squad.
"The U-21 national team's coach, Nenad Gracan, accepted the request of Nikola Vlasic and freed him of this representative action," they said.
When asked about a possible Everton bid Kos told Split newspaper Slobodna Dalmacija: "The transfer window runs until August 31, sometimes transfers happen a minute before midnight.
"We don't want to lose one per cent of our quality. We also have to think about financial stability."