Initial talks have already taken place between Fulham and representatives for the 18-year-old, according to Marca, with Pitarch said to be open to following his former coach to the Premier League.
The move would follow the potential arrivals of Gonzalo Garcia and Cesar Palacios, two more Real Madrid academy products who are set to join Fulham this summer in a combined deal worth around €50m for 70 per cent of their rights.
Pitarch progressed through the age groups under Arbeloa, from the Under-19s to Castilla and eventually into the first team last season, making 10 league appearances and featuring six times in the Champions League, including starts against Manchester City in the last 16.
With Arbeloa having since left for Fulham and Jose Mourinho now in charge in Madrid, Pitarch's path back into first-team contention looks uncertain, with the club currently viewing him as a Castilla player for the coming season despite his breakthrough campaign.
Any deal is likely to take longer than the swift arrangements for Gonzalo and Palacios, however, with Pitarch currently recovering from a knee injury that is expected to keep him out for several weeks.
Fulham are also exploring other midfield options, including Southampton's Shea Charles, valued at around €30m, giving the club room to be patient.
Marca reports Real Madrid would want in excess of €20m for Pitarch, whose enthusiasm for a reunion with Arbeloa is seen as a significant factor working in Fulham's favour whenever talks do move forward.
Born in Fuenlabrada, Pitarch is regarded as one of the standout prospects to emerge from Real Madrid's academy in recent years, with the club having previously discussed tying him down to a longer contract to protect against exactly this kind of interest.
His willingness to follow Arbeloa mirrors the pattern already set by Gonzalo Garcia and Cesar Palacios, both of whom viewed regular first-team football in England as a more attractive prospect than fighting for a place behind Mourinho's senior options in Madrid.