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The market is reportedly starting to heat up for superstar outfielder Bryce Harper, though he isn't biting just yet.

According to Jon Heyman of the MLB Network, Harper has already turned down "multiple" offers exceeding $300 million:

And so the Harper saga continues.

The Phillies, according to multiple reports, remain the frontrunners for Harper, though it might come at a significant cost:

And Todd Zolecki of MLB.com reported that "the Phillies and Boras have been talking more regularly lately and making progress, but that they were not close to a deal. Another source said Tuesday that the Phillies had a second face-to-face meeting with Boras early last week in Florida."

Andy Martino of SNY, meanwhile, has reported over the past two days that Harper to the Phillies may not happen at all:

And the San Francisco Giants reportedly remain in the running, though it's unclear just how serious they are as contenders for Harper:

The 10-year, $300 million contract that Manny Machado reportedly signed with the San Diego Padres on Tuesday, per Mark Feinsand of MLB.com, gives Harper a baseline in his own negotiations. And per Heyman's report, several teams have recognized that and put out offers at that level of money.

It's certainly possible, of course, that Scott Boras fed those numbers to Heyman to create the perception of a more vibrant market for Harper than actually exists in an effort to increase his leverage with any interested teams during negotiations.

The last thing the Phillies would want to do, for example, is bid against themselves. If they believe they are doing so, they can draw a line in the sand with the belief they have the best offer on the board and that Harper will eventually relent and take it.

But a vibrant market for Harper—or at least the perception of one—could inspire the Phillies to increase their bid. Of course, the Phillies could also call Boras' bluff, if it is indeed a bluff. That's the game of chicken Boras is playing with the Phillies, and any other interested teams.