Hernandez moved to the Bernabeu on a season-long loan last summer and found his first-team opportunities limited until last week, when Madrid coach Carlo Ancelotti was hit with several injuries to key players.
The 26-year-old has stepped up to the plate in magnificent fashion, scoring three decisive goals in two important games, and Madrid are now weighing up the possibility of signing him on a permanent basis.
According to Spanish newspaper Marca, Madrid???s purchase option, which is set at ???20m, must be activated by Thursday.
However, Madrid are unwilling to meet that valuation and want to negotiate a new deadline and fee with Manchester United.
United are thought to be open to extending the deadline to allow more time for Madrid to make a decision.