The on-loan star has had no assurances from the Blues hierarchy and a variety of issues need to be resolved before the Croatia international can be signed on a permanent deal.
Kovacic has made 41 appearances, without scoring, since arriving at Stamford Bridge on a season-long loan deal from Madrid last August.
There is no pre-agreed buy-out clause open to the Blues, meaning they would need to agree on a deal with Los Blancos, though the Spanish capital club are not expected to resist a sale.
There is also the future of Maurizio Sarri to consider, which could affect the status of the midfielder's future. The Italian boss may have started well in west London, but a lack of consistency in form and results since then has seen his methods questioned.
Furthermore, the Stamford Bridge club's recent transfer ban means securing permanent deals for Kovacic and Gonzalo Higuain is not currently at the top of the agenda.
As things stand, Chelsea will be unable to sign players for the next two transfer windows as they await the outcome of an appeal after FIFA sanctioned the club for breaking the rules over the recruitment of foreign minors.
Previously, clubs like Real Madrid, Barcelona and Atletico Madrid have had their bans suspended in the short term, pending the result of a final outcome, but Chelsea have not been granted this option.
The Premier League side face a race against time to have their ban postponed, with their appeal to be heard on April 11. If a positive outcome is not reached at the first attempt, they will move on to the Court of Arbitration for Sport.
However, it is understood that the Turkish giants are currently going through something of a financial crisis and will hold off on agreeing a fee for a player who has scored twice in eight appearances until the end of his 18-month loan deal.