Sources told ESPN.com that the Nets, amid fears that they'll be unable to re-sign Shaun Livingston in free agency, have identified Jack as a prime target to either help fill the void or improve their backcourt versatility.
After arriving in Brooklyn in a mid-season trade with Sacramento, Thornton has only one year left on his contract, which would appeal to the Cavaliers as they attempt to create as much salary-cap flexibility as possible for the summer of 2015.
Brooklyn, meanwhile, is among the few teams in the league believed to be unafraid of trading for the two fully guaranteed years left on Jack's contract. Jack's contract is only partially guaranteed in 2016-17.
The Nets, sources say, are already weighing their backcourt options because they're concerned about losing Livingston to a richer offer than league rules will allow Brooklyn to make in free agency after Livingston exceeded all expectations last season playing on a minimum contract.
Because it is so far into the luxury tax, Brooklyn is limited to offering Livingston a three-year deal worth just over $10 million.