The 19-year-old caught the eye of the Wenger during last year’s under-19 European Championships and was subject to Arsenal interest in the winter.
Wenger is thought to be prepared to spend £11 million on bringing the Castilla star to the Emirates Stadium.
Parejo said: "For me, it is a compliment that such an important European team is showing interest. I have heard rumours but my intention is very clear - my dream is to succeed in Madrid.
"Nobody dislikes something like that (being compared to Cesc Fabregas) but I prefer to look in the mirror and see Raul, Guti and Iker Casillas, three footballers who have come out of this youth system and have gone on to triumph in Madrid. I am young and I have patience."