I set my price because that's what I think the item is worth. I won't mention offers because that immediately lets potential buyers know you're willing to drop it. That doesn't make sense to me. If anyone wants to PM an offer that's fine, I can agree or disagree, incorporate a trade item etc. Not putting a firm price seems counterintuitive, like going to the supermarket to buy a lemon for 30p but them letting you know they'll accept 25p.
I put "or near offer" in a sale thread once. Unless you are desperate to sell, and are really willing to take anything anyone offers, I don't think it is a good idea. In my case I was selling an expensive knife (£300+) and had a number of people trying it on in short order, making "offers" up to 30% less than I was asking, less than a day after I had put it up for sale. I wanted what I was asking but it it didn't shift in a couple of weeks I would have considered taking 10-15% less. But the offers came in immediately, and some people were pushy, and then unfriendly when I said I didn't want to accept their offer at that time.
What is not acceptable is setting up your sale to be an auction. You have to be clear about the price you want to aim for.