The 27-year-old forward managed just eight Championship starts for Hull last season after an injury kept him sidelined for much of the campagin.
However, the forward netted a remarkable eight goals in that time, and was one of the Tigers' top performers when he was fit.
Since joining the club from Palermo in 2014, he has made 99 appearances and produced an impressive return of 36 goals.
Hernandez has struggled with injuries during his four years in England, and was one of the players Newcastle considered prior to signing Joselu in the summer.
An Achilles’ injury sustained in mid-August ruled Hernandez out for six months and made the Magpies turn their attention elsewhere, his agent Pablo Bentancur confirmed at the time.
The Spaniard managed just four goals in 30 appearances for the Magpies - half the goals of Hernandez in three times the number of games.
Despite Hull's attempts to retain the striker, the Uruguayan confirmed on social media that he was set to leave the club this summer, amidst a flurry of interest from clubs across England and the continent.
Although Hernandez has 27 caps to his name and 11 international goals, his recent injury record and lack of match time this season has seen him miss out on a place with his country at the World Cup.
As a result of his status as a free agent, Hernandez is understood to have joined Rafa Benitez's 50-strong shortlist of possible forward options for Newcastle this summer.
However, Benitez is believed to want to sign a proven top-level forward, meaning Hernandez is unlikely to be a priority target.Though, should Newcastle sell either Dwight Gayle or Joselu - alongside the likely departing Aleksandar Mitrovic - then the club will seek an additional striker.