I don't believe he's obligated to talk to Mueller and I think his lawyers have recommended against it. From what it looks like, Mueller isn't even investigating Trump for collusion with Russia at this point, he's just looking for something/anything he can pin on him that'll give Democrats a reason to bring up impeachment hearings. I also think Mueller might be trying to get himself fired because he knows his investigation is going nowhere and the outrage his firing will bring might be enough for impeachment.