The report claims Wednesday are keen to trim their £25million-plus wage bill this summer, as two of their highest earners attract interest from rival clubs.
Stoke are described as being 'big admirers' of Fernando Forestieri, the Argentina-born forward who ended last season with five goals from six starts, while Middlesbrough and Birmingham are 'believed to be tracking' Barry Bannan, according to the Star.
Bannan, the Owls' string puller in central midfield, was a reported target for Birmingham during last summer's transfer window.
Despite Sheffield Wednesday's predicament, the Star adds that 'it remains unclear whether the Owls’ hierarchy would entertain offers for the pair', whose March returns catalysed their side's surge up the Championship table.
Stoke have already spent close to £20million on two new signings, Oghenekaro Peter Etebo and Benik Afobe, since their relegation from the Premier League, although Middlesbrough and Birmingham are themselves thought to be wary of breaching Financial Fair Play regulations after heavy spending last summer.
Could Sheffield Wednesday lose Forestieri and Bannan?