Toffees boss Ronald Koeman got a first hand view of the Croatian during their recent Europa League qualifier.
The Daily Mailclaims that the deal could be worth up to £8m.
Hajduk's manager Ivan Kos admitted on Monday that Vlasic could be sold before Thursday's deadline and the Croatian Football Federation confirmed on Tuesday that he had been allowed to leave the U21 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.
It is believed Everton will most likely loan out Vlasic straight after the deal is completed.