It depends a lot upon the niche you're blogging in and how engaged your readers are, but expect sponsors to want your traffic to be at around 5,000+ monthly readers (or more). That can take some time to achieve. For example, here's a snapshot of my first year of traffic (in orange) when I started blogging—and my second year of traffic (in blue):
As you'll see, my first year of blogging saw only about 9,000 total readers, but in my second year, you'll see traffic begins to pick up dramatically as I start to figure out who my audience is and which traffic strategies work best for me. It was at this point, once my readership grew to around 10,000 monthly readers (on average), that it became a viable option to start doing sponsored content.