Final Cut Pro (along with virtually every other Pro-level edit software) is not compatible with mp3 files directly.
You must first convert an mp3 to an AIFF file, then import only the new AIFF file.
iTunes does a great job of this.
Here’s how… its really fast once you set up iTunes the first time like this:
iTunes> Preferences > Importing > Import Using: AIFF Encoder> Custom> 48.000 kHz, 16 bit, Stereo >OK
Drop your mp3 into iTunes window.
Select (highlight) the file you want to convert, then:
Advanced (Toolbar Menu)> Convert Selection to AIFF
iTunes will create a new file (in seconds) with the SAME NAME as the original, but ending with .aif
You can set up a special folder for iTunes to send it to, or just use Search to find where it “defaults to” on your HD.
Drag this new .aif file into your open FCP Browser.
The actual .aif file will (and can) stay in the iTunes folder, just its “reference” icon shows in the FCP browser.
It will play and edit just as any other media file in FCP.