The exact amount and term for Jake is probably a work in progress for management. Have to believe 100% they want to sign him, but difficult to predict his value, given his history here, and inconsistency in his production at times. Wouldn't doubt they're revaluating Jake on a game by game bases, and will take as much time as they need to make the right offer for them.
Overall, he produces well enough now with potential for more, and plays a responsible all round game. Definitely would not lump him into the category, if he's not producing what is he doing type of player. Because of that, think he'd be a fairly hard player to replace.
Saying this, it's all up to Jake if he wants to be here. Maybe he just wants to move on from the history, clean slate. Although, think it would be best if he did stay, as time goes on, he'll have every opportunity to be successful, and be a leader on this Bruin's team if he really wants it.