There are many ways that landlords and property managers advertise the rental of their property, including a fixed price or 'make an offer' and even auctions for rental properties where potential tenants bid against each other for the right to lease the property.
The best thing to do is ask the property manager or landlord what level of interest there is in the property and how soon you need to move on securing it.
If you have been doing your homework you will know how the property compares to others you have seen, and this ultimately becomes your best decision making tool.
If the property is in high demand, then it is unlikely you will have much if any room to negotiate because there is always someone else ready to take it and any negotiation tactics may backfire against you as the landlord may think you are unable or uncomfortable to pay the rent and go with another applicant on the shortlist.
Honesty is the best policy if you really like a place because landlords and property managers like to deal with people they can trust. Your honest and open approach might just make you the person out of a number of applicants that the landlord chooses.
If you think the property is in less demand, you can try to make an offer and see how it is accepted. It is not uncommon for landlords to negotiate especially if they like your references.