City had to play 17 year old Chris Gunter at right back last Friday after losing Kerrea Gilbert to injury and seeing James Chambers return to Watford. Wright will enhance Dave Jones' options ahead of the game at Sheff Weds.
Wright has just a few games under his belt this season, two for Sheff Utd, one of which was against Arsenal at the Emirates Stadium and one game on loan at Leeds Utd.
Wright was at Aston Villa for 8 years between 1995 and 2003 making 256 Premiership starts.
Today is the last day for loan signings so expect more news later.