Glasgow Rangers forward Joe Dodoo has left Ibrox for Charlton Athletic on a season-long loan.
Chris Wood has joined Burnley from Leeds United in the summer transfer window.
Charlton could face competition from Wigan Athletic for O'Shea, who helped Sheffield United to the League One title this season.
The right-back moved to Ibrox during last summer's transfer window but has appeared just once under new Rangers boss Pedro Caixinha.
Bradford City's out-of-contract winger Mark Marshall has been linked with Charlton Athletic and manager Karl Robinson has hardly dampened speculation.
Ibrox outfit Glasgow Rangers should look at former Gers player Alex Rae, suggested Charlton Athletic manager Karl Robinson last month.
The Charlton Athletic boss took a risk on the midfielder at MK Dons.
Ibrox club Glasgow Rangers are reportedly interested in outgoing Tottenham Hotspur recruitment chief Paul Mitchell.
Ibrox outfit Glasgow Rangers should look at former Gers player Alex Rae, suggests Charlton Athletic manager Karl Robinson.
The Charlton Athletic winger is set to join Everton in January but hopes to follow in the footsteps of Tottenham Hotspur midfielder Dele Alli by returning to his current club on loan.