The 24-year-old is one of the most promising players in Croatia and is being tipped to follow Luka Modric out of Dinamo Zagreb.
Modric joined Tottenham in a huge £16.5million deal - but Vukojevic would cost less than a third of that.
It is reported in Croatia that Dinamo are bracing themselves for a £4million offer from Celtic - although is far from clear whether the club would accept that.
Vice-president Zdravko Mamic is open to discussing a deal - but it seems he may wait until after Euro 2008 - when the player's value could rise significantly with a good performance.