The France international is ready to leave St James’ Park this summer following the Magpies relegation from the premier League to the Championship.
Several clubs have already shown an interest, including Borussia Dortmund, Roma and Paris Saint-Germain.
However, according to Diario Madridista, it is Real Madrid who are at the front of the queue after opening formal negotiations for Sissoko.
The Spanish side are ready to offer £25million for the midfielder – but Newcastle are still hopeful they can bank closer to £35m.
Sissoko is keen for the move to go ahead and Real are reportedly ready to use add-ons or even loan players to get a deal over the line.