The 16-year-old was born in Croatia but has been based in London for the last five years.
Vekic is also coached by David Felgate, who looked after Tim Henman's early development as a professional.
She told reporters: "No, I'm very happy playing for Croatia. Us Croatians have big Croatian hearts so we go out there fighting on the court, fighting for our country.
"Me and David have been together for about five years and we clicked from the start. I listen to everything he has to say and he's always right."
Vekic confirmed her status as one of the game's brightest young talents by winning her first-round match in Melbourne earlier this week.