The 20-year-old was one of Ronald Koeman's summer signings, joining for a fee of £8million from Croatian side Hajduk Split and has been one of the Toffees shining lights in a side that have fallen way below pre-season expectation.
Vlasic made only a substitute appearance against Lyon during Thursday night's 3-0 loss in the Europa League, replacing Aaron Lennon in the 71st minute.
Making eight appearances for the Toffees, Everton's number 27 has scored one goal for the Merseyside club against Group E opponents Apollon Limassol which helped Unsworth's side gain their only point of the Europa League campaign so far.
Everton fans have taken to Twitter to plead with caretaker manager Unsworth to start the young attacker, with one fan claiming that if the Toffees start with Vlasic then they "will win".
Depends on the 11 picked , if Vlasic and lookman start then we will win .— Danrowley USM (@mreverton2015) November 2, 2017
Expect luck to change Sunday with a win. Picking team not easy but Lookman, Baningime, Vlasic must start. Keane, Jags, Rooney to return— Jason Tooley (@Jason_Tooley) November 2, 2017
Must start Lookman Vlasic wide— DolphinsVoice / NSNO (@voice255) November 3, 2017
Must not start Jon Jo Kenny he's not up to it yet. Holgate as holdover til Coleman
5. Jury out Sandro Klasan
Easy v Watford start vlasic Lookman , Benni , Davies and DCL— Danrowley USM (@mreverton2015) November 2, 2017
-Schneiderlin should be dropped.— Tom (@thomass__14) November 2, 2017
-Williams should be dropped.
-Lookman shoud start every game.
-Vlasic should start every game @Everton
Some players should be on from the start. Vlasic is one of them. He's too young and motivated to benefit from wonder-sub label— Steve (@bionictype1) November 2, 2017
V Watford... 4-1-4-1... Pickford.. Kenny jags Keane Baines.. Baningime.. Vlasic Davies Sigurdsson Lookman.. With Rooney up top, stay up top!— UTFT..NSNO (@nickcarr49) November 3, 2017
My team vs Watford:— Man like Muhamed (@barebesic) November 2, 2017