Everything is typically always negotiable. However, in a negotiation, you usually have to be offering something of value to the other party, in return for what you are asking for. Additionally, how much the owner is going to be willing to negotiate will be determined on their specific situation, and what comparable properties are renting for.
If they are asking $2000, and everything comparable to the property in the area is renting for $2200, then don't expect them to budge much. Also, is the property vacant, and if so, how long? Does the owner "need" someone in there to cover the mortgage, etc. - or can they afford to "hold" out until they get what they want?
Also, what are you offering them? Spotless credit? A longer lease? A bigger deposit? Excellent references?
Consideration of all of the above will determine how "willing" an owner will be to work with you and the monthly rental amount.