Leeds United have made the 27-year-old one of their top targets this summer but face stiff competition to land his signature with the Uruguayan leaving the KCOM stadium after four seasons with the Tigers.
Hull confirmed in a statement on their official club website that an offer had been made to Hernandez that "exceeded what the Club would normally offer at Championship level" but the forward has opted to move on with his contract expiring on June 30.
"The striker will now look to make a fresh start elsewhere and we would like to wish him well for the future," the statement continued.
Hernandez joined Hull from Palermo in 2014 for a club-record fee, Â£10m, having just missed out on a Â£20m move to Aston Villa after failing to agree personal terms.
The forward missed most of the 2017/18 season with a ruptured Achilles tendon but still managed to amass eight goals, despite playing just 10 times, as City avoided a late relegation scare.
United want a proven, UK-based striker to lead their line next season and Hernandez has emerged as a leading option this summer.
Leeds also have first refusal of Carpi striker Jerry Mbakogu, a Â£4m deal which was agreed in January, but as revealed by club president Stefano Bonacini the option will expire on June 30.