The academy graduate had been one of several names on a list drawn up by Álvaro Arbeloa as he looks to strengthen his new club, but Real Madrid's refusal to even open negotiations has made the deal unworkable.
Sources at Valdebebas are said to rate the midfielder highly, and with José Mourinho keen to have him available for selection this season rather than sanction his exit, a move was never seriously entertained by the Spanish giants.
Pitarch is in the closing stages of his recovery from an injury sustained after Spain's Under-19 European Championship triumph in Wales, which has kept him out of Mourinho's first-team plans since the setback.
He is expected to feature for Real Madrid Castilla in the coming weeks, despite remaining registered as a first-team player, as part of a gradual reintegration designed to have him ready for when the manager needs him, following an absence of close to two months.
Arbeloa already has a track record of shopping in the Real Madrid academy this summer, having brought Gonzalo García and César Palacios to Craven Cottage in deals worth a combined £43m (€50m). García has scored in his last two matches for the Cottagers, and Arbeloa's familiarity with Real Madrid's youth ranks means Fulham are unlikely to be finished raiding his old club before the window closes.
With Pitarch off the table, attention has turned to Manuel Ángel, another Castilla product who was given opportunities by Arbeloa during the closing stages of last season before his move to Fulham.
According to reports in Spain, Cádiz have entered the race for the midfielder with an offer of around £3.4m (€4m), the same fee Fulham would need to match to sign him. A battle for his signature is expected to intensify as the transfer window nears its close.
Fulham's priorities for the closing days of the window lie elsewhere, however, with the club understood to be focused on bringing in two central defenders as they look to address what Arbeloa regards as the squad's most pressing area of weakness.