The England international still has just under five years remaining on his contract in North London, but that has not prevented the 21-year-old from being linked with a transfer to a European giant.
According to Don Balon, Real are one of the clubs who hold an admiration for Alli and they are prepared to propose a swap deal involving Mateo Kovacic.
The 23-year-old has only made 37 starts for the Champions League holders in over two years at the club, while the Croatian international has spent just 63 minutes on the pitch in La Liga this season.
Real would have to pay a sizeable fee on top of including Kovacic, but it has been suggested that president Florentino Perez wants to strengthen Zinedine Zidane's squad after a poor start to the season.
The La Liga champions are already seven points off the pace in Spain's top flight.