No you can't download voicemails, maybe your mobile network can try and arrange something for you on special request, but its not really a thing that exists on mobile devices as its not recorded locally unlike landlines. You can save the voicemail, that will stop it being deleted or over written in the meantime until you can contact your mobile network for more information. Or you can simply record it yourself using another device, such as by plugging it into a pc using a 3.5mm male to male jack.