Silva's departure ends a five-year stint in west London that included a top-half Premier League finish last season and established him as one of the most respected coaches outside the traditional top six.
His move to Lisbon was set in motion by a chain reaction higher up Spanish football's coaching carousel. Jose Mourinho's return to Real Madrid freed up the Benfica job, while Real Madrid's vacancy was created by the exit of interim coach Arbeloa.
Arbeloa, 43, had been placed in interim charge of Real Madrid in January after Xabi Alonso was dismissed midway through the season, overseeing the side through the remainder of the 2025-26 campaign.
The Spaniard's path to that position came through six years working in Real Madrid's academy system, where he progressed through various age groups before being promoted to first-team duties.
Sources have indicated to ESPN that talks between Fulham and representatives for Arbeloa have taken place, though the discussions are not yet at an advanced stage.
As a player, Arbeloa made two spells at Real Madrid and also had Premier League experience with both Liverpool and West Ham United, giving him a working knowledge of English football.
Fulham are understood to have explored other candidates as well, including former Ipswich Town manager Kieran McKenna, though that route has effectively closed.
McKenna would have required an £8million release clause to be triggered before he could leave Ipswich, and he has since departed the Suffolk club entirely, citing a desire to spend time with his family.
Other names linked with the Fulham vacancy include Lille's Bruno Genesio and former Villarreal boss Marcelino, both of whom carry significant top-flight experience in European football.
Fulham finished 11th in the Premier League last season under Silva, a campaign that saw the club continue to establish itself as a stable top-half presence after returning from the Championship.
The west London club face an important summer regardless of who takes charge, with forward Raul Jimenez departing and the futures of Harry Wilson and Samuel Chukwueze also unresolved.
Whoever succeeds Silva will inherit a squad in transition, and Fulham's hierarchy will be eager to move quickly to avoid a managerial vacuum disrupting preparations for the new season.