Deform sphere help!

Hi, first time poster and new to using Unity here. I have something of an odd task that needs accomplishing and was wondering if anyone has any tips or advice about how to go about it.

I need to create a sphere that will bend in on itself when it collides with another object. Much like this image.

1490668--83183--$ivf_2342241b.jpg

As I’m new to Unity I have no idea where to start and any tips would be appreciated.

Check this demo for starters,

It has mesh deform examples.