If you really want someone then being honest and straight forward is best. If it really is your best offer tell them and you can honestly explain you have no room for negotiation. If you claim it is your best offer, then allow negotiation you look dishonest.
To go lower and see if the applicant is available for a little cheaper might save you a few $1000 on salary but at the cost of potentially losing the applicant.
People appreciate honesty and companies that don't play games.