In order to embed an image into a DGN file, the required screenshot of the Google Earth Image should be taken, and saved as a Paintbrush Picture. The Image can then be Inserted this object into your DGN file.
It can be achieved by using the tool:
> Edit > Insert Object > PaintBrush Picture
The Google Earth image can then be added to the DGN file.
Please be aware that this process can increase the file size.
Also, when saving the file as a DWG this process is not supported.
It is recommended to use Raster Manager for inserting raster files into a DGN.