The 18-year-old is currently at Croatian outfit Hajduk Split, and has made eight league appearances for the club so far this season.
Both Chelsea and Tottenham are keen on landing him in the January transfer window, while Lazio, Napoli and Liverpool have also been linked with making a move in the past.
Despite attracting interest from some of Europe's biggest clubs, his father Nikola Mujan insists he will stay put for now in order to develop his game.
"I must admit a number of clubs are interested in Tonci. Some years ago he got a call to come to Liverpool, but he stayed," he told newspaper Slobodna Dalmacija.
"Now there are more clubs from England who want him, and also from Italy.
"But for now he wants to stay at Hajduk and become an even better player. But then again we have to see what kind of plans his club has for him."
Chelsea have been keen on luring the best young talent across Europe to Stamford Bridge in recent seasons.
If he does join Chelsea, it is likely that he will be farmed out on loan to Vitesse Arnhem, where a host of Blues youngsters are currently cutting their teeth.
Tottenham meanwhile have seemingly been extensively scouting Croatia, having been linked with Dynamo Zagreb's Alen Halilovic in recent seasons, as well as his former team-mate Tin Jedvaj, who joined Roma last summer.
Indeed, Tottenham are said to have had a bid for the pair turned down before the close of the summer window.