The 19-year-old attacking midfielder, who can also operate as a winger, impressed against the Blues over two legs for Hajduk in the Europa League.
He played well enough for Ronald Koeman and Steve Walsh to sanction a move that could be worth over £8 million pound move.
Vlašić joined the Croatian giants at age 12 and has shot up the ranks ever since. He has amassed 12 goals and 20 assists in 112 senior team appearances for Hajduk since first breaking into the first-team.
The attacker was expected to be called up to Croatia’s squad for the European Championships in 2016 but injuries denied Vlašić his chance. He made his debut for Ante Čačić’s team in May of this year against Mexico.
The jewel of the Croatian talents?
Vlašić has been labelled the jewel of the Croatian youth system but is yet to develop as he was expected to during the early days of his rise.
In 2014, the youngster was a part of The Guardian’s ‘Next Generation: 40 of the best young talents in world football’ series after reportedly being of interest to Chelsea, Real Madrid and Tottenham Hotspur.
He has stayed and continued his development in Croatia despite other highly-rated talents like Andrija Balić and Mario Pašalić moving elsewhere in Europe.
Now, Niksi - as he's known in his home country - looks set to follow his fellow countrymen in a move away from his homeland.
Everton looking to do late deals
Koeman is looking to be busy as the transfer window comes to a close, despite already bringing in 12 new players at Goodison Park.
The Blues are still on the hunt for a striker, with Koeman stating that signing a forward is his priority before Thursday.
Diego Costa is the target of a potential loan move after reports in Spain suggested he could he join Everton until January before heading back to parent club Atletico Madrid.
Koeman is also looking to sign a left-sided defender who can play centrally and as cover for Leighton Baines. Ramiro Funes Mori is the ready-made player for Koeman but he sustained a knee injury in pre-season and will miss the whole of the 2017-18 Premier League season.