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Madonna, Alex Rodriguez

Brian Zak/Sipa Press via AP images; Kevin Mazur/ Getty Images

Madonna's only four days removed from her quickie divorce from Guy Ritchie, but the Material Cougar doesn't seem to be wasting much time on the singles scene.

E! News has learned that the 50-year-old Queen of Pop enjoyed the cozy company of 33-year-old rumored boytoy Alex Rodriguez during a late-night private flight Monday, with the keep-'em-guessing couple arriving in Miami in the wee hours this morning.

The duo departed from Atlanta Monday, shortly after Madonna completed the Georgia stop on her Sticky & Sweet Tour and landed just before 2 a.m.

"They got right into an SUV and drove away," a source at Miami's Signature Airport told E! News. "They didn't want anyone to see them."

Leave it to Madonna to ensure her flights of fancy include an actual flight.

Madonna, and presumably A-Rod, are expected to stay in Miami for a few days, shacking up in a secluded mansion.

The trip will combine both business and, one would assume, pleasure. The now two-time divorcée is set to perform to a sell-out crowd at Miami's Dolphin Stadium Wednesday night.