The Brazil attacker's current deal runs to 2027, leaving him less than 18 months away from committing to a pre-contract with a foreign club ahead of departing in a Bosman transfer.
The Athletic says Real's attempts to discuss new terms have been stonewalled by Vini Jr's camp, with the major stumbling block being his relationship with coach Xabi Alonso.
Vini is yet to be convinced by Xabi, particularly after being hooked during their El Clasico victory over Barcelona earlier this month.
Adding to the speculation was the decision to start Vini on the bench for the draw at Elche on Sunday.
Vini's situation is being monitored by Europe's biggest clubs, with Liverpool, both Manchester clubs and Chelsea watching developments closely. PSG are also keeping tabs on the situation, though any move for the fiery Brazilian will depend on coach Luis Enrique's approval.