Yes. You can do it using the Track Matte and a white circle (or drawing a white circle in Title Adjustments workspace).
1) Put your video on Video 1 and a duplicate of it on Video 2 directly above the first.
2) Add a Blur or Mosaic effect to the video on Video 2.
3) Place a white circle graphic on Video 3 or use the Title Adjustments to draw on on Video 3.
4) Keyframe the position and size of the white circle so that it follows whatever you want to blur.
5) Apply the Track Matte to the video on Video 2 and set it to use Video 3 as its matte position.
This is one of the most popular of the 50 effects I take you step by step through in my "Cool Tricks & Hot Tips for Premiere Elements 14" book, available on Amazon -- if you're looking for detailed instructions with illustrations. You can also learn more about the book and see demos and tutorials of a number of its effects on this page: