There's a couple reasons you'd sign White early. However , it's a year early, so I wouldn't consider it until next year. One is, reward a player that has out performed his rookie contract and protect against him playing careful in his final year. Second is, while you'd have to calculate the difference in re-newing his contract vs his rookie contract pay a year early, you'd likely pay less per year vs waiting.
Next year? Absolutely not and it's not even a discussion, they will not do that.