The 17-year-old Slovenian has been making quite a name for himself in his homeland - allowing him to draw admiring glances from afar.
Zabret made his senior debut in the Slovenian Premier League last season at the age of just 16.
His potential was noted by a number of clubs, and he took in a spell training with Swansea in January.
It is understood that they have now fended off interest from sides across Europe to strike a deal with Domzale.
Zabret is expected to fly into the UK on Monday to finalise personal terms before flying off to Holland with the rest of the Swans' first team squad later in the week.