The youngster did want to leave on loan to get regular first team football.
However, manager Pep Guardiola and others at the club convinced him that he would develop better by staying at City.
He stated, per the Manchester Evening News: "There's a lot who have been good with me. Walks, Nathan Ake, Rodri when he was fit was good - we had conversations - but one I've spoken to quite a bit recently would be (Mateo) Kovacic and Bernardo. The way they think, they know exactly what the manager wants.
"Pep is always giving information and pointers. There is always room for improvement, little tiny details that make a massive difference at that level. I try to take on board as much information as possible.
"It's always been about just playing my game, nothing more needs to be done. It's what I want and what the managers want, just to dictate the play, keep everything simple and give it to the wingers who can deliver with their fancy tricks and that.
"I'm training in and around the first team and hopefully if I keep performing as I am I'll get my chance and then it's about me taking it."
"There was obviously temptation - there always is going to be - but when the manager and staff around him want you to stay and be around that first team there's not much of a choice," Wright added.
"There's no temptation any longer when you get the information that they want you to stay and be around it because they see you as someone that could be around it. The temptation went out the window as soon as I heard that: I was staying for the season."