The Jays have until November 14th to negotiate exclusively with Burnett, after which he is an unrestricted free agent, as per the Canadian Press.
This situation is a bit of a tricky one for the Blue Jays. On the one hand, whatever money they (potentially) dole out will certainly amount to overpaying Burnett, even though Burnett was probably one of the ten best starters in the American League this past season. However, I can't imagine that Burnett is a great bet to repeat this year's perfomance, nor that he gets signed for less than $15 million a year and 4 years at this point. He turns 32 in January, and in four years his contract will likely be a drag on whomever employs him.
On the other hand, the Jays rotation for next year without Burnett is basically Roy Halladay, Jesse Litsch and some combination of David Purcey, Scott Richmond, John Parrish and others (with perhaps McGowan joining later). This transforms a Jays rotation that was arguably the best in baseball last year to a middle of the pack one, when the Jays theoretical window of contention - if it exists - is closing.
Tough decisions will be made, and I imagine that the Jays would be happy to sign Burnett to another two years past their orginial commitment; Burnett by all indications doesn't seem one to go for a steep hometown discount though. We shall see.