Bild reported that Arbeloa's management contacted Leverkusen's sporting leadership — chief executive Fernando Caro and sporting director Simon Rolfes — about the possibility of taking over from departing head coach Kasper Hjulmand.
The pair declined, with the club's position reportedly that the Spaniard had not demonstrated sufficient evidence that he could lead Leverkusen back to the level they achieved under his compatriot Xabi Alonso.
Arbeloa took charge of Real Madrid's first team on an interim basis in January after the club dismissed Alonso, seven months into what had been billed as a long-term project at the Bernabéu.
He was unable to arrest a second consecutive trophy-less season and confirmed before the campaign's end that he would not continue as permanent head coach. José Mourinho has been appointed as his designated successor on a three-year deal.
Bayer Leverkusen's search for Hjulmand's replacement has been the most troubled managerial hunt of the current summer. Filipe Luís, the former Flamengo coach, was identified as their first-choice candidate but chose AS Monaco instead. Andoni Iraola was the second option but he has agreed a deal with Liverpool. Oliver Glasner, who left Crystal Palace after a trophy-laden two-year spell, has been linked with AC Milan. All three top candidates have effectively chosen other destinations.
Kicker has reported that Leverkusen are now leaning towards a surprise candidate whose name has not yet entered wider circulation — a development that suggests the club may be preparing to move in an entirely different direction from the high-profile names they pursued unsuccessfully.
Leverkusen finished sixth in the Bundesliga last season, missing Champions League qualification entirely. The appointment of the new head coach is considered the most consequential decision the club will make this summer, with multiple transfer decisions — both incoming and outgoing — dependent on the identity and tactical preferences of whoever gets the job.