David Ornstein and co-author Guillermo Rai reported the talks on Wednesday, describing Arbeloa as available following the conclusion of his spell at the Bernabéu and as having held a face-to-face meeting with Fulham's decision-makers.
Arbeloa, who spent the majority of his playing career as a right-back for Real Madrid and Liverpool, moved into coaching within the Madrid system after retirement, working his way through the youth setups before being appointed head of the Castilla reserve team. On January 12 he was promoted to the first-team role as an emergency measure, replacing the sacked Xabi Alonso.
His six months in charge produced the Champions League quarter-finals — where Real Madrid were eliminated by Bayern Munich — and a LaLiga challenge that faded after a strong mid-season position. He left the club by mutual consent this week following the appointment of José Mourinho.
For Fulham, the vacancy arose from an unexpected source. Marco Silva left at the end of his contract to succeed Mourinho at SL Benfica, ending a five-year association in which he guided the club back to the Premier League and established them as consistent mid-table finishers.
Arbeloa has management experience at the highest level but only in a limited and emergency context. The question for Fulham's ownership — the Shahid Khan family — is whether six months at Real Madrid, however brief, represents sufficient pedigree for a permanent appointment at a club that has built something real in the Premier League and cannot afford a backward step.
The process is ongoing. Arbeloa has met. Nothing has been agreed. But the fact that the conversation has happened at all places him firmly inside the frame.