Ravel Morrison has returned to parent club West Ham from Cardiff City on compassionate leave.
Brighton boss Sami Hyypia is weighing up a move for former France captain Alou Diarra.
The 35-year-old signed from Preston last year, but did not make a first-team appearance during Roberto Mancini's final season.
Although he did feature during City's post-season tour, the experienced shot-stopper is expected to be Manuel Pellegrini club's third-choice behind Joe Hart and Costel Pantilimon.
Wright began his career at Ipswich 18 years ago and went on to make over 230 first-team appearances before joining Arsenal in 2001.