I don't know if Brown is formally doing that, but it's no secret whom he wants to win.
Considering that Strickland is running for reelection and is far more of an institution than the recently-elected Brown, it's not going to be a death brawl with the personalities involved (I think). At the very least, I expect it to get a lot more ferocious for the GOP primaries in Florida, Kansas and Missouri as of now.
Other than Kansas (which I expect to be deadlocked between Tiahrt and Moran), the GOP primaries in MO and FL should be smooth sailing barring something strange happening.