HITC Sport understands that the Owls are readying an offer for the free agent, but face competition from across Europe for the midfielder.
He joined Wigan from Cardiff City earlier this year, and he is now locked in talks with a number of sides.
HITC Sport has been told by sources that Wednesday – an ambitious outfit harbouring promotion aspirations in 2015/16 - are gearing up a bumper offer to try and entice him to Hillsborough, offering him an immediate step up back into the second tier of English football.
There is Premier League and Championship interest in Kim, but there are also options for him abroad.
Clubs from France, Spain and Germany have all contacted him, so he has an important decision to make regarding in which direction he now wants to take his career.