The experienced Spaniard – who used to play for Liverpool – is rumoured to be available after losing his starting berth to Dani Carvajal, with Los Blancos said to be keen to do business before the transfer window closes.
Arbeloa is said to have fallen out with manager Carlo Ancelotti, and at 31 there appears to be no way back for him.
A return to England suits the 56-time Spain international, after he enjoyed an impressive spell at Anfield before joining Real in 2009.
Chelsea and Arsenal have been alerted by the situation, and are both thought to be eyeing late moves.
Jose Mourinho coached the defender during his time at the Bernabeu, with speculation suggesting he could go back on his claims that he is not looking at further signings to link up with the experienced defender.
Arsene Wenger is also keen, with Arbeloa’s abity to fill any role across the backline tempting for the Frenchman.