Watkins, an England international, is being considered by the Magpies as a replacement for Callum Wilson, who has left the club after his contract expired last week.
Manchester United is also reportedly interested in Watkins, with the intention of adding him to their attacking lineup alongside recent signing Matheus Cunha from Wolves.
Notably, Arsenal had previously attempted to sign Watkins in January but ultimately decided to pursue Sporting CP centre-forward Viktor Gyokeres instead.