This is absolutely possible. You just need to cancel your personal Deutschlandticket membership, which is a monthly subscription, and then sign up for a new one using NAVIT. This way, your subscription will be managed through NAVIT starting from next month.
Please note that if you canceled your ticket before the 10th of the month, it will be processed by the end of the same month. Cancellations made after the 10th of the month will be handled by the end of the following month, in accordance with the Deutschland Ticket policy.