An attacking midfielder, Halilovic made history when he became Dinamo Zagreb's youngest ever player at 16 back in 2012.
Having played in the Champions League with Zagreb, he became the second youngest ever player to feature in the competition.
He went on to play 44 times for the club, scoring seven goals, before being lured to Spain by Barca.
And he would make history again when he made his international debut at the same age, under Bilic, against Portugal in a friendly match to become the country's youngster ever player.
Both manager and player moved on to pastures new since. But now the Hammers are hoping Bilic's established relationship with the player will bode well in their attempts to persuade him to move to the Premier League.
Messi blocking Halilovic's first team progress
After shining for Barca's B side, Halilovic made his first appearance for the senior team back in January, replacing Adama Traoré for the last 28 minutes of a 4-0 away win against Elche CF in the last 16 of the Copa del Rey.
Barcelona only signed the player last year on a five-year deal so question marks would be raised as to why they are willing to let him leave.
But with Messi still relatively young there would be no room for such a similar player in the European Champions' midfield for the forseeable future.
So Halilovic, who is unerringly similar to the Argentine great in his dribbling style, may see his future elsewhere and Barca are believed to be willing to let him leave as long as the Catalan giants have a buy back clause.
Hammers set for biggest coup of recent years?
If the Hammers pull off the transfer it could become one of the coups of recent years.
The transfer would not be a case of co-owners David Sullivan and David Gold taking a punt on a youngster that has failed to fulfill his potential elsewhere like a Ravel Morrison.
If they land Halilovic West Ham would be getting a player genuinely considered one of the greatest and most impressive youth talents in European football.
Halilovic: the lowdown
Watching Halilovic you could be forgiven for thinking it is Real Madrid star and compatriot Modric twisting and turning in midfield. And not just because they are of similar size an build with wavy blonde hair, but the obvious immense quality with the ball at their feet.
The youngster is left footed and has an abundance of skill as well as a powerful shot in his armoury.
He can, and has played out wide as a winger, but his future could well be in the middle of the park where his trickery, creativity and supreme quality in one-on-one situations could unlock even the meanest defenses should he continue to progress.