The media outlet claims the former Sunderland midfielder is in advanced negotiations over a move to the Tigers, after being released by the Mackems at the end of last season.
City began their season with a 1-1 draw at Aston Villa on Saturday.
And that's because Larsson would bring just as much off the pitch as he does on it, a combination which should significantly benefit Hull in their quest for an immediate return to the Premier League.More news: Nissan Leaf - specs leak shows new drivetrain will have 148bhp
Larsson, who started out in England at Arsenal, spent six years at Sunderland after joining in 2011 from Birmingham.
The 90-cap Sweden global is the sixth arrival at the KCOM Stadium as Leonid Slutsky plots a return to the top flight, with the Tigers having joined Sunderland in suffering the drop last term.
He becomes Championship club Hull's seventh summer signing, following the arrivals of Michael Hector, Callum Burton, Ola Aina, Fraizer Campbell, Kevin Stewart and Ondrej Mazuch.