Jim Antle at American Spectator mentions Rand Paul for president rumors, and quotes the Kentucky senator as saying merely that "he won't run against my dad," Rep. Ron Paul (R-Tex.).
As I've heard many a rumor that the Ron Paul 2012 campaign is gearing up and could be very close to an official announcement, this sounds to me like a denial.
Antle thinks that isn't necessarily the best news for the cause of limited government in national politics:
The case for Paul running is that he's simply a better politician than his father and would move the ball farther than either Ron Paul or Gary Johnson could. As a senator, he'd have the luxury of four years to mend fences with Kentucky voters. Paul could bring the constitutionalist message to the forefront of the Republican primary debates without getting sidetracked into theoretical discussions of libertarianism.
I disagree with the above. Ron Paul, as one of the few people ever to win election to Congress as a nonincumbent three different times (I don't know of any others but haven't checked every congressman ever's record on that), is obviously a very good politician indeed. He has gotten very far since 2007 in creating a national movement of donors and activists, skewing young on at least the latter, for a very outre brand of politics. I see no evidence whatever, despite him perhaps looking more conventionally like a "slick professional politician," that Rand is a better politician than his dad. (And I think Ron's stumbling earnestness and lack of polish makes him a more successful politician for those very reasons.)
In my experience, Ron inspires far more wide-ranging actual admiration and affection from people who don't agree with his whole message than does his son. (See center-left-leaning men's mag Esquire on how "it's impossible to not like Ron Paul" and Paul as a top-10 congressman.) Ron's ability to stress that military spending should be first on the budget chopping block before government spending that fills the pockets of the less well off should also help him escape the "evil Republican" trap if he's reaching out beyond GOP faithful for support. Rand, for whatever reason, has not shown any crossover appeal that I've seen.
Also, I'm sure the son would be just as apt to get "sidetracked into theoretical discussions of libertarianism" as the father if he became a more prominent public figure. (Remember the Rand Paul campaign civil rights controversy.) I say: Ron Paul 2012, Rand Paul 2016 (if necessary).