What I mean is if you have a server, Create a custom basemap showing only the area of interest. Then publish the basemap.
I do not believe you can take an esri basemap and create a rectangle or draw the area you want downloaded.
See this post for a how to. Use a Area of Interest to build the tpk. But also note as I posted in here that the Export tool has a bug in it. It may be ok for collector but not sure. My guess is you would do the workflow of use Manage Tile Cache then Export to turn it into a tpk. Sideload this as a basemap.