Four-time Champions League winner Ancelotti is facing an increasingly uncertain future in the Spanish capital as Real continue to fall behind Barcelona in the La Liga title race.
Following a 3-2 defeat at the hands of Villarreal on Saturday, Real could find themselves 15 points off top spot if Barca win their game in hand against Girona on Monday evening.
Ancelotti guided Real to La Liga and Champions League glory last season, and Los Blancos are still in contention to retain their European title as they prepare to meet Chelsea in the quarter-finals later this month.
Ancelotti is contracted to Real until the end of next season and has voiced his desire to remain at the club for as long as possible, but a Champions League elimination could plunge his future into further doubt.
Both Brazil and Chelsea are thought to be keen to hire Ancelotti if he departs Real Madrid this summer, so Los Blancos are drawing up plans for life after the four-time Champions League winner.
According to the Daily Mail, youth team coach Arbeloa is now high up on the club's shortlist to take the reins this summer, and he has leapfrogged B team head coach Raul in the race to become Los Blancos' new head coach.
The 40-year-old, who retired from playing at the end of the 2016-17 season, took up a youth team coaching role in 2020 and oversaw a run to the UEFA Youth League quarter-finals earlier this season.
Real's Under-19s took 16 points from 18 against Celtic, Shakhtar Donetsk and RB Leipzig in the group stage before beating Red Bull Salzburg 3-1 in the last 16, but they were eliminated in the quarter-finals with a comprehensive 4-0 loss to AZ Alkmaar.
As well as the possibility of Arbeloa taking control as first-team manager, Real could also look to appoint the Spaniard as number two to Jose Mourinho, although such a move would not be unanimously supported within the club.
Arbeloa enjoyed two separate stints with Real Madrid from 2003-06 and 2009-16, winning a total of nine trophies, including two Champions League crowns.
The 40-year-old - who was also part of Spain's Euro 2008, World Cup 2010 and Euro 2012 winning squads - made 238 appearances for Los Blancos in all tournaments, scoring six goals and providing 15 assists.
Arbeloa ended his second spell at the Bernabeu in 2016 before joining West Ham United on a free transfer, but he only made four appearances for the Hammers before retiring at the end of that season.
Real are believed to have earmarked former Bayern Munich boss Julian Nagelsmann as their top target to replace Ancelotti, but the German will not make a decision on his future before the summer.
All of Chelsea, Tottenham Hotspur and Paris Saint-Germain could also try to hire Nagelsmann, though, and the 35-year-old is said to prefer a new job in the Premier League.