You need a smaller aperture to create a greater depth-of-field, but DoF is also dependent on camera-to-subject distance and focal length. You can use any DoF calculation app to do the actual calcs for your situation.
Once you start playing around with the app you'll know if you will be able to achieve the look you want. Let's try an example using Photobuddy for IOS:
100mm focal length
Canon 5D Mk III (full frame)
12 feet camera-to-subject distance
You need infinite depth of field for a sharp background (a far limit of infinity). Photobuddy tells me I'd need f/128 to get there. Sadly, my best lens in that focal length only does f/22.
So, if I instead plug in f/22 and see what that does for DoF, Photobuddy tells me that the DoF will be ~47 inches. No bueno for what you want. If I go to an 85mm lens, the DoF gets slightly bigger -- by a few inches.
OK, so let's play with subject distance. If I go to 30 feet, then DoF at f/22 goes up to ~300ft. But still likely not enough for what you want.
You get the idea. What you are trying to do may not be possible given the space, lens and composition constraints that you have. But using an app to explore will give you a sense for what is possible.