The 22-year-old has indicated he would like to stay with the Social on a long-term basis.
But the Welton player also hinted he may be prepared to wind down his contract if Social do not offer him the package he feels he deserves.
Carter, who has been at Social Park for five years, said: "My agent has been into the club for a chat and we are now waiting for them to come back to us with an offer.
"I have worked hard to get where I have and to help the club and I believe I deserve a new contract offer.
"You never know what sort of contract you are going to be offered. It's got to be right for me and for my family and we will see what the club comes back with.
"If it's not right for my family then I will play the season with the Social, hopefully help to win the Premier League and then see what my options are next summer."
Carter added: "Of course, it would be nice to sort things out this summer.
"If the club come back with the right offer then I would be happy to sign a new contract.
"I have enjoyed my time here and hopefully the fans appreciate what I have done at the club. We have a really good team spirit and I have always considered myself to be a team player."