The 16-year-old - scorer of a wonder goal in Hamilton's 1-0 weekend victory over Morton - has been watched several times this season by the Primera Liga giants, says the Daily Record.
Accies' youngster is also being tracked by another top Spanish side, Deportivo La Coruna.
Liverpool have already had a cash offer for him rejected.
"At most games we get around four scouts from various clubs but last week we had about 20. All the big names were represented.
"James is scheduled to make his 40th appearance for us against Dundee United at Tannadice in the CIS Cup this week and that tells its own story about the progress of a 16-year-old."