As answered previously the CD needs to be encoded in mp3 format and the easiest way to do this is by using a computer.
Unless your mp3 has a record facility with a line in socket which will enable you to record the sound directly from the cd player using a cable. Most mp3s with a sold record facility refer to the ability to record using a (poor quality) built in microphone which is ok for speech but will give disappointing results with music.
bit busy now ... so can't look ... but I'm guesing that some of the fancy music centers will have cd to flash or sd (in mp3) recording - one of the guys here says his dab radio does it
(record and play) - so you'd guess that it's logical for other devices to do it also