Adobe Illustrator in CS 6

I am a technical writer and use Adobe Illustrator in CS6 just enough to develop some basic shapes w/ colors that I need for my client template development in Framemaker. I am currently working on a template for a client. The client has an image that is available in both a .bmp format and .jpg format that I would very much like to use in the FM template. That said, I unfortunately need to upsize the image and w/ it being raster art, it obviously is too pixelated to use. Is there a way in AI that I can convert this image to the .ai format so that I could have it in vector format so resizing is not an issue?

FWIW, I was just mucking around w/ the image and saved both formats to a PDF but then when I opened the PDF for either format and enlarged the image, large parts of the image were still showing as heavily pixelated . . . so obviously the original resolution of the image is not that good. The client is a small client w/out a lot of formal processes, so they can't give me any information about how the image was initially created, its resolution, etc.

I know I might be grasping at straws here, but I am definitely very much a not quite fully functioning beginner w/ AI, so I figured the question was at least worth asking.

Thank you!

TVB