I can tell you exactly what I would do because I'm going through this right now. Some background: one of my tenants is asking to break their lease early because they purchased a house; they still have 6 months remaining on the lease. They gave me about 6 weeks notice of when they think they'll be closing and when they'd like to move out. They've been great tenants some I'm happy to work with them to find a solution that works for both of us.
Obviously it's in both mine and the tenants' best interest to find a new renter to ensure there is no gap in occupancy. I immediately marketed the unit for rent and also told the tenant they have the right to find their own subletter, so long as the new tenant meets the standard requirements I set forth for all renters (credit, criminal, etc). Remember, the current tenant is still obligated to fulfill their duty to the lease they signed, so if neither of you are able to find someone, it is still the current tenant's responsibility to pay the rent. With that said, I wouldn't suggest a specific timeline like you mentioned because if you're unable to find a new tenant it'll be you that is left holding the bag.