The 28-year-old midfielder was a massive part of the Inter side that won the league last season and has continued to remain pivotal for the club.
But he will be out of contract at the end of the season and negotiations over a new deal are yet to lead to an agreement between the club and the player.
Brozovic wants his new contract to reflect his importance in the team, but for the moment Inter have been reluctant to meet his wage demands, with newly rich Newcastle now showing interest.
However, the club want to sort out the sideshow of the contract negotiations soon and, according to Italian daily Gazzetta dello Sport, Inter want the midfielder to give his answer by the end of the year.
The Nerazzurri want to hold on to him and are prepared to put in extra effort to keep the Croatian.
But they do not want the negotiations to drag on for months and cast a shadow over the season.
Therefore, Inter want Brozovic to either sign a new deal by the end of the year or indicate his desire to leave.
The Serie A giants would consider selling him in the January transfer window if a new deal is not agreed upon.