The 20-year-old has endured a difficult 18 months at Ibrox since making the switch from Liverpool, managing just 10 first-team appearances due to a catalogue of injuries.
The former England Under-19 captain returned to full training on Monday following a calf problem and will hope to have finally put his health issues behind him.
The Daily Record are now reporting that League One high-flyers Wigan are ready to offer Rossiter a fresh start by taking him south of the border with the Latics ready to table a relatively low offer.
Light Blues boss Graeme Murty must now decide whether to stick with a player who showed a lot of promise at Liverpool or cut their losses after his tough time with injuries.
West Ham United are reportedly weighing up a summer bid for Amiens forward Moussa Konate.
Bordeaux are reportedly close to agreeing a deal which will see Malcom join Inter Milan on loan with a view to a permanent deal.