The Birmingham Mail says the Baggies have been linked with the player for some time and have now followed up their interest in the 21-year-old, who spent last year on loan at Watford, by making a proposal to the Italian club.
A representative of the player said: "West Brom have made a bid and they interest Matej.
"He is focused on Udinese but West Brom are a club he would like to join.
"We have heard good things about Steve Clarke from other players. And West Brom are clearly a club going places."