Nah - he's very comfortable working with a DoF. He brought in Zidane at Real Madrid to do that job. As long as he has a say in who it will be then I don't belive its an issue for Jose.
There were plenty of rumours he didn't get on well at all with Emenalo at Chelsea. You are right though in that the relationship is key. Perhaps if the club make a move for Koeman then they could do worse than approaching Les Reed from Southampton as well - they seem to have a forward thinking and positive relationship. This article is quite interesting about how they work if it hasn't been posted.
http://www.telegraph.co.uk/sport/football/11366206/Gary-Neville-The-era-of-the-gaffer-is-over.html