I think it depends entirely on Jose. If he likes working with a DoF or not isn't known. I read a book about his time at Madrid (pretty interesting read) and in it it said that Jose wanted complete control over everything at the club like Fergie used to at us.

This lead to Jose clashing with Perez and their DoF at the time as some of the decisions weren't agreed with by Jose. Also at the time Jorge Mendes was pretty influential at the club and had such a say in transfers that you could consider him a DoF in a way. However as we all know a DoF is more than just someone who handles transfers like Mendes.

My overall point being that I think Jose will want complete control at United as well, we are a club who always gives the managers control, except in the case of LVG who just wanted to coach. If we were to appoint someone it'd be someone who Jose could trust. Remember his digs at Chelsea when they signed Djilobodji instead of Stones about how they were signed by someone who he trusted, which looking back now could be considered sarcastic.