The precocious Croat is on the radar of the Catalan giants but his current club were unhappy with the conditions proposed by the Blaugrana
The Croatia international has impressed for Dinamo this season, and the club were quick to rebuff any interest from the Liga side during the January transfer window, with reports suggesting the Catalan club offered €3.6 million (£2.9m) plus bonuses for the 17-year-old.
However, Mamic believes that Barca are determined to ensure a transfer goes through for Halilovic, whose contract expires in the summer.
"We have received an offer from Barcelona, but it was not accepted because neither Dinamo nor the Halilovic family were entirely satisfied with conditions proposed by Barcelona," the director told Jutarnji List.
"But I am sure that we haven't heard the end of this, Barcelona are persisting to ensure that the transfer takes place.
"Frankly, I would like Halilovic to remain at Dinamo for three more years."
Halilovic has a growing reputation in the game and has also attracted reported interest from Premier League pair Tottenham and Arsenal.
The precocious talent has made 13 appearances for Dinamo this season, helping them open up a five-point gap at the top of the table from rivals Hadjuk Split.