Autonomous suturing has been a long-sought-after goal for surgical robotics. Outside of staged environments, accurate localization of suture needles is a critical foundation for automating various suture needle manipulation tasks in the real world. When localizing a needle held by a gripper, previous work usually tracks them separately without considering their relationship. Because of the significant errors that can arise in the stereo-triangulation of objects and instruments, their reconstructions may often not be consistent. This can lead to unrealistic tool-needle grasp reconstructions that are infeasible. Instead, an obvious strategy to improve localization would be to leverage constraints that arise from contact, thereby constraining reconstructions of objects and instruments into a jointly feasible space. In this work, we consider feasible grasping constraints when tracking the 6D pose of an in-hand suture needle. We propose a reparameterization trick to define a new state space for describing a needle pose, where grasp constraints can be easily defined and satisfied. Our proposed state space and feasible grasping constraints are then incorporated into Bayesian filters for real-time needle localization. In the experiments, we show that our constrained methods outperform previous unconstrained tracking approaches and demonstrate the importance of incorporating feasible grasping constraints into automating suture needle manipulation tasks.