Although reports from Teeside claim Middlesbrough are leading the race for Gravesen, who is set to leave Spain within the month, the 30-year-old Danish international prefers a move to Tyneside.
He has already rejected a switch to Celtic and Everton, but Glenn Roeder has already added to his growing band of midfield players by signing Damien Duff.
Roeder is desperate to sign a striker, and there is only so much money he can splash around until he sells the likes of Boumsong and Luque.
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