The tour comes as part of the Marlins' attempt to sell the free-agent left-hander on signing with Florida. With a new downtown ballpark, the Marlins are going after some big free agents, including reportedly hosting shortstop Jose Reyes Wednesday.
The White Sox aren't out of the running for Buehrle, but various reports have the Yankees, Red Sox, Rangers and Cardinals interested in his services.
Guillen always has been quick with praise for the easy-going lefty. Buehrle has been viewed as a fit in South Florida because of his relationship with Guillen, the fact that the Marlins are looking for a veteran lefty, and that they have money to spend and want to use it on pitching.
In 2011, Buehrle notched his 11th consecutive season with at least 200 innings pitched, 10 victories and 30 starts, a franchise record and the longest such active streak in baseball. Only Buehrle and CC Sabathia have recorded at least 10 victories for 11 consecutive seasons.
The White Sox always have planned on having other teams set Buehrle's value before deciding if the fan favorite fits into a 2012 budget that has little to no wiggle room.
While that is the same tactic the White Sox used last season when ultimately re-signing Paul Konerko, there appear to be longer odds when it comes to keeping Buehrle.
The biggest stumbling block is that the White Sox are intent on reducing a payroll that went above $127 million last season. When Konerko was signed, the White Sox were committed to raising payroll to acquire the talented they desired.
Information from ESPNChicago.com's Doug Padilla was used in this report.