Blackburn Rovers have signed midfielder Jay Spearing from Bolton on loan until the end of the season
Rotherham have brought in Crystal Palace defender Jack Hunt on loan until the end of the season.
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."