Forum Moderators: not2easy
I probably should have asked why in my original post - if your printer/designer is requesting your image (is it a logo or illustration?) in .ai or .eps then the answer to your question will be a bit different...
They need it this way to preserve its clarity - simply saving a JPG as either will not be what they require as it is a compressed raster image
They are probably looking for a vector so that the printed results are 'perfect' on any scale - unless the JPEG is 300DPI and the dimensions of image on page are relatively small...
If not you can ignore me ;)
I've never used it, so I don't know how good it is, but it could be what you're after if you don't have one of the more expensive packages.
OK it won't export to a .ai which is what you asked for, but it will export to a number of other vector formats which should suit your needs.