Let me take a crack at this for you...When you client asks for a .ai file, I assume they're asking you to submit the art as vector paths rather than a raster image (pixels). JPEGS and TIFFs are raster images.
Simple answer: Can't be done unless you (a) redraw and recolor image using Illustrator's vector-drawing tools (Pen, Pencil, and shapes tools), OR (b) apply Live Trace.
Live Trace literally traces groups of pixels, which gives you a mass of vector paths that, realistically, cannot be reshaped. Live Trace also creates huge files sizes. For these two reasons, I don't care to use Live Trace, but happily, I'm pretty good with the aforementioned tools, so I'm able to avoid Live Trace.
To see how inaccurate Live Trace is, in Photoshop draw a black circle with a white fill. Save it as a JPEG or TIFF, place it in Illustrator, and apply Live Trace. Zoom way in on the image to see what you have. Positively makes you want to learn to use the vector-drawing tools.
It's possible that the client is familiar with the types of vector files generated by Live Trace and may be satisfied with them.
I would suggest that you place your JPEG or TIFF in Illustrator then apply Live Trace, and send a sample to the client to see if this is what they want. Of course, there are a raft of options when creating a Live Trace image. You'll probably just have to play with the options to figure out what you want. Don't look for thorough, exhaustive, detailed documentation on Live Trace options. It doesn't exist. It will require a lot of time playing with them to see what they do.
Your time might be better spent learning how to use the drawing tools.
PS: The only thing in Live Trace that I find indispensible and extremely cool is the option to create a Swatches palette from the raster image.