United won their Premier League International Cup tie 2-1, with the match highlighted by a wonder goal from Guruzeta.
The midfielder fired Bilbao in front with a stunning volley, before James Wilson and Ethan Hamilton scored to secure the points for United.
The 21 year-old is out of contract at the end of the season and can move without a fee.
Premier League sides will need to pay training compensation to bring him to England but it would be fraction of his market value.
Newcastle boss Rafa Benitez is also an admirer of the youngster, who can play as a winger or striker, and could join the race to sign him.