Mr Green, 77, and his wife, 75, were being driven to a hotel in Cala Bona when they were caught in the floodwaters, newspaper Diario de Mallorca reported.
Muddy waters rushed down roads, houses were flooded and vehicles piled up on top of each other after the Mediterranean island was pounded with rain in just a few hours, video footage showed.
Some of the victims were found still in their cars that had been carried away by the flood waters.
Bauza told Cadena SER radio that two other victims were local residents, including an elderly woman whose body was found in the basement of her house.
Spanish tennis icon Rafael Nadal has taken part in a clean-up operation in his native Majorca after the region was hit by deadly flash floods.
Spanish Prime Minister Pedro Sanchez said during a visit to the eastern coast of the island that the impacted area would be declared a "zone of catastrophe", which unlocks funds for recovery, reconstruction and compensation of victims.
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Rescue workers reportedly found the vehicle submerged and on its side at the mouth of the torrent in S'Illot at 2am (1am BST) on Wednesday.
"It all happened in less than 10 minutes", an unidentified witness with wet clothes and a blanket over his shoulders told TVE.
The UK Foreign Office is supporting families of two British people who are among those to have died.
The Balearic Islands' emergency services spokeswoman, who wasn't authorized to be named in media reports, told The Associated Press that the body of a Dutch woman was recovered from the garage of a house in Arta, another nearby town. "We had to swim to try to survive".
At least 10 people have died in the floods.
The 17-time Grand Slam victor also provided shelter at his tennis academy in Manacor for displaced people whose homes were severely damaged by the flash flood.
Sanchez will be flying to the area later Wednesday, his office said.