The 22-year-old has established himself as a regular starter for the Allsvenskan club over the past two seasons and has attracted attention from across Europe as a result, with Girona, Wrexham, Mainz 05, Rangers and Schalke all previously credited with interest at various points.
According to Ontheminute.com, Hull's interest is still at an early stage, with the newly promoted Premier League club considering whether to follow up with a formal bid.
Fulham and Southampton remain in the picture too, though it is not yet clear what fee would be required to prise Skoglund away from Hammarby. The Swedish club find themselves in a strong negotiating position regardless of who moves first, given Skoglund is contracted to the club through to the end of the 2029 season.
Hull have already been active in the Swedish market this summer, having signed compatriot Elliot Stroud from Mjallby earlier in the window, a deal that suggests the newly promoted Tigers are willing to compete financially for Scandinavian talent as they build a squad for their first Premier League campaign in years.
Skoglund's form this season has done little to cool the interest. He has three assists from 16 Allsvenskan starts and has one goal in 15 caps for Sweden's under-21 side, numbers that continue to make him one of the more closely tracked right-backs outside Europe's top five leagues heading into the closing stages of the transfer window.
Interest from Italy has also emerged in recent days, with Torino credited with considering a move, though no bid has yet been tabled and Hammarby's sporting director Mikael Hjelmberg has said the club are not currently in negotiations with anyone over the player.
Hammarby had previously knocked back an offer from Lecce worth around €1.5m, and with the Allsvenskan title race still live, the club's timing on any sale is likely to be as important as the fee itself.