The Clarets' one-time record signing is approaching the end of his current deal and would become a free agent in the summer.
But Paterson, 25, has dropped a clear hint that he wants to stay put and show his best form after overcoming a series of injuries.
"At the moment talks are ongoing and they've been ongoing for a while now. I think it will come to a head very soon," he told the Lancashire Telegraph.
"I think unfinished business is the right way to put it. I don't think Burnley fans have seen the best of me.
"My best football possibly for Burnley was in the Premier League. I was possibly at the top of my game. When I came back from my knee injury it was probably the best I've been at."
He added: "It's unfortunate for me I haven't forced my way through this year. I'd like to show the club what I am now compared to what I was when I first came. It's up to me."