A qualifying offer is a one-year, $14.1 M deal, and if the player rejects it and signs elsewhere, the former team would get a compensation pick. Burnett has been deciding between retiring and returning to the Pirates, so it doesn't seem likely that he will sign elsewhere. If Heyman's report is true (the team has until 5 PM EST to submit an offer), then the Pirates must be banking on the fact that they're the only team in the running for Burnett.
UPDATE: The Pirates, via press release, confirm that no qualifying offer was made.
Here are the players around baseball who have received qualifying offers, along with a few notable players who didn't receive offers.
Tim is the owner and editor in chief of Pirates Prospects. He started the site in January 2009, and turned it into his full time job during the 2011 season. Prior to starting Pirates Prospects, Tim worked with AccuScore.com, providing MLB, NHL, and NFL coverage to various national media outlets, including ESPN Insider, USA Today, Yahoo Sports, and the Wall Street Journal. He also writes the annual Prospect Guide, which is sold through the site. Tim lives in Bradenton, where he provides live coverage all year of Spring Training, mini camp, instructs, the Bradenton Marauders, and the GCL Pirates.