The Arsenal legend has stated that he turned down the a job as manager of the Robins because he does not feel ready to take over at a club looking for promotion
Wright, 49, is currently the first team coach at League One side MK Dons and was approached for the job before former Liverpool player Kevin MacDonald took up the position on Thursday.
The former England international is settled in the south east with two young children, and says another factor in why he allowed the opportunity to pass was that such a move would have meant uprooting his family.
Wright told The Sun: "I got a call on Monday morning and it was something that, all of a sudden, I had to start thinking about other things.
"You start thinking about what team you will put out if you're going to do it. I was very, very excited about it.
"But in the end it was something that, being out the game for the time I have and only being back at MK trying to learn certain things, it's not enough to time to go into a club like that and try to get them what they need right now — promotion."
London-born Wright played for a host of clubs in the 1980s and 1990s, most notably at Crystal Palace and Arsenal, where he was the club's record goalscorer until overtaken by Thierry Henry in 2007.
"They've got a very, very good man in Kevin MacDonald," Wright added. "But it was something that I was really, really enthused about. The wife wasn't keen. I explained it to her over how it could be."