I was doing some reading on this, and I can't find the article now, but it suggested that Trump would use executive orders to dissolve the inquiry.
Rosenstein, for all his issues, has made it clear he wont fire Mueller, and the person next in the chain of command from him is even less likely to do what Trump wants (crazy Cruz supporter). Trump will have to pull the trigger himself, which is possibly the only thing that has stopped him so far.