Masterson is said to be out of contract at Anfield this summer, which means rivals clubs could sign him for training compensation.
And the newspaper claims the 20-year-old could be tempted by the opportunity to kick-start his senior career at Norwich, who currently sit top of the Championship and appear destined for the Premier League.
Masterson joined Liverpool's academy from the Dublin-based Lucan United in 2013.
But despite playing regularly for the Reds' Under-23 and U18 sides - often as captain - the Republic of Ireland youth international is still awaiting his senior debut.
The Norwich links to Masterson come just days after Liverpool were credited with an interest in one of the Canaries' own centre-backs, Ben Godfrey.
Could/should Norwich make a move for the Liverpool youngster?
Have something to tell us about this article?