Ilicic, who has scored 16 goals in 79 appearances for Slovenia, last played for his country in November 2021 and since then has left Serie A side Atalanta to return to Slovenian club Maribor, having suffered with mental health issues.
His performances this season, scoring eight league goals in helping Maribor finish second in the standings, have earned him a chance to finally play at a major tournament.
Kek named a 30-man squad, so will need to cut four players before naming his official list. Slovenia have two friendly matches with Armenia and Bulgaria before heading to Germany where they face Denmark, Serbia and England in Group C.
Benjamin Sesko of RB Leipzig, Slovenia's top scorer in qualification with five goals, is also in the squad along with 31-year-old Atletico Madrid goalkeeper Jan Oblak.
Squad:
Goalkeepers: Jan Oblak, Vid Belec, Igor Vekic, Matevz Vidovsek
Defenders: Jure Balkovec, Jaka Bijol, Miha Blazic, David Brekalo, Vanja Drkusic, Erik Janza, Zan Karnicnik, Petar Stojanovic, Zan Zaletel
Midfielders: Timi Maks Elsnik, Adam Gnezda-Cerin, Jon Gorenc Stankovic, Tomi Horvat, Jasmin Kurtic, Sandi Lovric, Benjamin Verbic, Miha Zajc, Adrian Zeljkovic, Nino Zugelj
Forwards: Zan Celar, Josip Ilicic, Jan Mlakar, Benjamin Sesko, Andraz Sporar, Zan Vipotnik, Luka Zahovic