The question should be: "would McKenzie want to come to GB?"
Before signing with the Saints, the Packers expressed their interest in him. He only had eyes for the Saints.
This time, I find it hard to believe that the Saints cut McKenzie without some 'win-wink, nod-nod' deal in place, where they cut him but promised him they'd resign him to a better contract or something (ala Banta-Cain of the Pats).
Cutting McKenzie after his solid performances doesn't make sense, unless he was raising hell in the locker room.
The NFL: Where Greg Jennings Happens.