Both Spanish giants have been linked with the 21-year-old, but Palermo's €70 million demands have deflated interest from Spain.
However, Pastore has said he will fulfill his ambition of joining either Madrid or the Blaugrana at some point in his career.
"I heard that Florentino Perez [Real Madrid president] has spoken plenty about me. Real Madrid and Barcelona are two of the most important clubs in the world, and the fact they are interested in me makes me tranquil and means I am doing well," Pastore told El Grafico.
"It would by nice to join a club like that as it would mean an important growth in my career. If things continue as they are then maybe one day I can play for a club of this category."
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