Sky Sport Italia's Gianluca Di Marzio reported in early June that Hull had won the battle for Stroud's signature, with Hull City owner Acun Ilicali also previously confirming in an interview with Hull Live that the winger was closing in on a move.
Speaking to Fotbollskanalen about the situation, Stroud acknowledged the toll the prolonged process had taken.
"It's obviously been a bit tough, with a lot going on and everything. But like I said, I'm just trying to let it go and be here in the present. Make the most of and enjoy the football, and everything I have here. It's been a bit tough but you have to make the best of the situation," he said.
Asked directly whether the move was close, Stroud added: "Yes, I think it is. Then how close, we'll have to see."
Stroud, whose contract at Mjällby was set to expire, has scored three goals and added an assist in 10 league appearances this season, nine of them starts, having emerged as one of the standout performers in Mjällby's title-winning Allsvenskan campaign last year — a first-ever league title for the small Swedish club, followed by Svenska Cupen success this May.
A left-footed, direct wide player known for his work rate and defensive contribution, Stroud began his career in Sweden's lower leagues at IK Oddevold before joining Mjällby in 2023, and earned his first Sweden call-up in March.
The move to Hull is reported to be worth around £3m and would see Stroud sign a four-year deal, joining a Hull side managed by Sergej Jakirovic that has been busy strengthening across multiple positions ahead of the club's return to the Premier League.
At 24, Stroud represents something of an unconventional route to the top flight, having worked his way up from Sweden's lower divisions rather than through a traditional academy pathway. His combination of pace and defensive discipline has drawn comparisons in the Swedish press to James Milner, and it was that all-round game that first alerted Genoa to his availability before Hull moved decisively to win the race for his signature.