Vipotnik, 24, scored 23 league goals last season as Swansea finished 11th in the Championship, nine points off sixth-placed Hull, who secured their return to the top flight via the play-offs.
The Slovenia international joined Swansea from Bordeaux in the summer of 2024 but managed just seven goals in his debut season in English football, before a significant improvement in his second campaign prompted him to sign a new contract with the Welsh club running until 2030 back in March.
West Ham and Strasbourg have also been credited with interest in Vipotnik this summer, though Hull are understood to be the first club to table a concrete offer, with a further bid expected in the coming days, according to The Athletic.
Swansea have already strengthened their own forward line this summer, completing the signing of Scotland international Ross Stewart following his departure from Southampton, while also retaining Republic of Ireland striker Adam Idah. Manager Vitor Matos has insisted he can keep all three forwards happy, telling reporters last week that Stewart's arrival was not related to Vipotnik's future at the club.
Hull relied heavily on Scotland international Oli McBurnie as their focal point in attack last season, and manager Sergej Jakirovic is keen to add further firepower to ease that burden as his side prepare for the step up in quality.
Vipotnik previously played under Jakirovic at Slovenian club Maribor as a teenager, a connection that could yet play a role should the Tigers return with an improved offer in the coming days.