Arbeloa accepted Fulham's offer to succeed Marco Silva at the start of July following the Portuguese coach's call to move on to Benfica.
The former Spain international saw out the second half of last season as interim boss at Real Madrid, following Xabi Alonso's chaotic exit, but he confirmed his desire to move on and take permanent role elsewhere.
Fulham completed a deal for Jonah Kusi-Asari prior to Arbeloa's arrival at Craven Cottage and he's now looking at two Real Madrid players as his first targets.
Franco Mastantuono and Gonzalo Garcia are both on his radar, amid uncertainty over their places in Jose Mourinho's plans in Madrid, and a double loan offer could be put forward.
Mastanuono made 35 appearances in his debut season n Madrid - the majority as a substitute under Alonso and Arbeloa - and the Los Blancos hierarchy are not looking to sell the 18-year-old at this stage.
However, 22-year-old Garcia is in a different position, with his path to the first team blocked by Kylian Mbappe and Vinicus Junior, and his starting chances will be limited by that in the months ahead.
With a contract in place until 2030, Real Madrid are in a strong negotiating position, and they are expected to demand in the region of £30M from Fulham to consider selling the Spanish striker.