Kovacic has scored six goals in 36 appearances for Dinamo, and became the second youngest scorer in Champions League history when he netted against Lyon in December.
The 17-year-old Croatian midfielder is being hailed as the new Luka Modric in his home country and he is seemingly set for superstardom in the not too distant future.
And Zagreb sporting director Zoran Mamic admits there is a possibility Kovacic could leave the club before the close of the transfer window at the end of the month.
"Like the club, the player is quiet but in football anything can happen," he told Tuttosport.
"We now have to wait and see over the next few days. But as of today he has not been sold to any club."
However, it was reported on Tuesday that the United boss had decided against launching a move for Kovacic, with Dinamo's asking price of £10 million deemed too expensive.
“Sir Alex has had scouts watching Kovacic regularly and really likes him, but it now seems they won't pay the money to make an acceptable bid,” a source told Goal.com.