Martinez has been on United's radar for more than a year and he starred against them for Bilbao in the Europa League this season.
Equally adept at centre-back or in central midfield, Martinez's versatility and ability on the ball has been noted by Europe's top clubs.
Liverpool, desperate to inject some life into their ailing squad, are also keen on the Spain international, who has a contract at Bilbao until 2016.
But the emergence of Madrid and Barcelona as potential suitors could swing any deal in the La Liga heavyweights' favour.
Martinez, 23, is settled playing in La Liga and the financial clout of both Madrid and Barca means they would have no problem in stumping up the perceived £40m it would take to land the star.