A former club official of los Blancos says the 21-year-old should be lining up against the Argentine in future clashes rather than playing alongside him
The Brazil star, who completed a move to Barcelona from Santos in May, had a trial in the Spanish capital as a 14-year-old in 2006.
However, Carlos Martinez de Albornoz, the club's general manager at the time, reportedly had reservations about paying the €60,000 (£50,000) requested by Neymar's agent Wagner Ribeiro to secure the services of the future star, which Giraldez labelled a "historic mistake".
"Neymar was willing to stay at Real Madrid. We even registered him in the city," he told Cadena Ser. "We saw that he was different.
"It was a historic mistake by Real. He could have been our Messi."
The 21-year-old netted his first competitive goal for the Blaugrana in the 1-1 draw with Atletico Madrid in the first leg of the Spanish Super Cup a fortnight ago.