I have heard that there is part of the sage's chackra inside of the nine tails.have you noticed when narutos in the nine tail form he has those marking s on his chest.i believe its the sage's chackra from inside of Kurama
If there's a relation between the two, like maybe Minato being a descendant and Naruto by default, then I can see it. In a way it's been hinted there's some relation between the two, though it might end up being symbolic.