During a three-year stay in the Spanish capital, Mourinho won one Liga title and the Copa del Rey and reached the Champions League semi-finals three times.
However, he left amid well-publicised reports that his relationship had soured with key players, including then-captain Iker Casillas and defender Sergio Ramos.
Mourinho has since returned to Chelsea and led the club to a Premier League and League Cup double last season, but a poor start to the current campaign has left his future in doubt, though the club's hierarchy are backing him.
Former Madrid president Ramon Calderon claimed that Mourinho is still held in high regard at the club, and Arbeloa believes a return remains a possibility.
"I've been asked before and I always say 'Yes, why not?'" he told The Independent . "He was a very important coach here.
"It is clear that because of the way he is, because he is very direct and he tells people straight, without hypocrisy, he upsets a lot of people.
"There are a lot of people waiting for him to fail but there are a lot more waiting to see him turn things around and move forward again. He's a very good coach, so I don't think the door at Real Madrid is shut to him, no."
Mourinho may have faced criticism this season, but Arbeloa remains full of praise for him and says he is like a "bullet-proof vest".