The Democratic and Republican nomination battles are still shaking out, but there’s a new twist in Hollywood political circles: New York Mayor Michael Bloomberg.

Bloomberg is drawing on his industry ties just as speculation centers on a possible independent presidential run.

Last weekend, Bloomberg played golf with CBS Corp. chief exec Leslie Moonves and dined with Walt Disney Co. CEO Robert Iger.

Of course, they are just meetings, and neither would necessarily be a Bloomberg supporter should he run; moreover, Bloomberg has not announced that he is running. In fact, he’s been known to get prickly when asked.

But last summer, in a visit to Los Angeles tied to a USC event on political bipartisanship, he dined with DreamWorks’ David Geffen, a major supporter of Barack Obama. And Bloomberg has deep ties within the industry because of his background building up a media conglom and because of his aggressive pursuit of TV and movie production in New York City.

The Republican nomination battle became clearer on Tuesday after John McCain edged out Mitt Romney to win the crucial Florida primary. Hillary Clinton soundly defeated Obama, although no delegates were awarded in their race after the state was stripped of its convention votes in a dispute with the Democratic National Committee.

Although Bloomberg has said he is not a candidate, his aides have been meeting with political strategists who specialize in ballot access and in third-party runs, as well as those who have worked for Gov. Arnold Schwarzenegger, one of Bloomberg’s best friends. A recent piece in New York magazine profiled deputy mayor Kevin Sheekey, his political strategist said to be plotting a presidential run for Bloomberg and setting up an operation. All that is needed, the piece maintains, is for Bloomberg to say yes.

Bloomberg could benefit from the increasing acrimony between the Clinton and Obama campaigns, especially if it gets bitter enough to spill over into tension among Hollywood donors. Geffen, for one, has already publicly expressed his dislike of the Clintons, so Bloomberg could be an alternative should Hillary be the nominee.

There’s also a benefit for entertainment executives who may back Bloomberg: He won’t be hitting them up for money, as he is expected to self-finance his campaign should he run. Their support would come in the form of seeking to win the backing of fellow media moguls.