Well, I'm totally confused. Are we working for the person being interviewed, or is he being interviewed by somebody else? Clearly, any situation needs control and care. We have a mumbling difficult subject (and keep in mind, I'm a Brit and have no idea who this guy is - but his real voice seems to be, well, a challenge) and he's seemingly unable to set up his end to make intelligibility the key feature?
We need a suitable mic, put in the right place, connected to the most appropriate gear - or anything is going to make him sound dreadful again. I'm assuming he is some kind of 'name', right? In which case, surely he has a collection of people who should be able to manage his sessions to make him appear at his best? If the interviewers are using noise reduction software - you really have to ask why? His voice is likely to be misinterpreted as noise in many circumstances. This needs human management at source, not repairs afterwards. However - is his horrible voice part of his character - the way that putting a low cut on James Earl Jones would rob it of it's authority, or putting a hi cut on somebody with a very high voice would spoil it? It's perfectly possible his voice is just misheard by the subject who actually might make it worse, but be unable to hear it?