As a player, Bilic spent four years in England with West Ham and then Everton.
The 39-year-old took over as Croatia boss in July 2006 after Zlatko Kranjcar failed to get the team into the second round of the World Cup.
Croatia will finish top of Group E if they avoid a 2-0 defeat against England or a loss by more than three goals.
They were unbeaten in this campaign until Saturday's 2-0 defeat in Macedonia.