Smith, who works for ESPN, is good friends with Jets coach Eric Mangini.
The Jets reportedly will send their first of two second round picks to the Bears in exchange for the 28-year-old Jones. The Jets will also receive a Bear draft pick in return.
But before the deal can be completed, Jones must pass a physical, something Cleveland's Lee Suggs didn't do last summer after a trade with the Jets.
Jones will give the Jets the feature back they have been looking for to replace Curtis Martin.