"We have a season-long agreement and that is how it stands," said O'Neill. "I know nothing about what someone else is reported to have said but all I do know is that the facts are that no one has spoken to me or, I believe, anyone from Aston Villa.
"We have an agreement, and we are happy with that agreement unless Liverpool come and speak to us about it, then that becomes a different issue.
"I am very happy with the deal. I think that Scott has done very well for us, he is a young goalkeeper with plenty of talent and Liverpool obviously recognise that. But at the moment the agreement is for the year."
Carson has spoken of his desire to stay long-term.
O'Neill added: "I have seen Scott quoted now and again. I have not exactly sat down with Scott. I think he is pretty happy in the role at this moment.
"He is enjoying his football, in fact he is vying even to become first choice for England which is fantastic, we are delighted with that. But I haven't sat down with him yet to talk about any long-term future."