The 19-year-old's current deal finishes at the end of the season.
"He could be a free agent soon but we want to keep him at the club which is the reason for this new contract," said club spokesman Brian Morris.
"We believe he and several other young players at the club are the future of this club and we want him to stay."
Carson has made just two first-team appearances against Chelsea and Manchester United in the Premier League last season.
"If a big club comes in you cannot stop the lad from moving, especially if it's a top Premiership club that came in for him," added Morris.
"We cannot say he's not for sale, but we are going to offer him a new contract and then it's entirely up to the lad if he wants to stay.
"If someone does comes in for in January and he decides he does not want to go, then it is his choice and we will be delighted with that."