Carson is currently on loan at Villa Park until the end of the season but is keen to stay after quickly adjusting to life with the Midlands club.
Carson said: "I think something has been agreed whereby, if everyone is happy, it could be made a permanent transfer.
"That's obviously up to the boss but it's something I would welcome. I want to establish myself as a number one and preferably I would like to do it here.
"I've been out on loan a lot over the past couple of seasons and it's not easy when you keep moving up and down the country. It would be nice to settle at a club that I like and where the fans like me.
"I've settled in well here at Villa. Everyone has welcomed me and that has been a big help. What I want now is to be settled for the next five to 10 years. I want to play as many games as possible."