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.
After opening his academy to flood victims, Rafael Nadal volunteered to help clear homes of water and mud.
Antonia Bauza, deputy mayor of Sant Llorenc des Cardassar, the worst-hit town, confirmed that two of the victims were British citizens.
Torrential rainstorms deluged the town of Sant Llorenc, about 40 miles east of the capital Palma, on Tuesday evening, with ten people being killed.
In an emailed statement, the British government's Foreign Office said: "We are supporting the family of two British people following their deaths in Spain, and will do all we can to assist them at this deeply hard time".More news: Dow Falls 430 Points as Bond Yields Surge and China Tensions Grow
MADRID-Torrential rainstorms caused flash flooding on the Spanish island of Mallorca, killing at least six people and leaving nine others missing on October 10, authorities said.
Witnesses said that within minutes a rush of water and mud from an overflowing creek had buried cars and torn down trees.
Two men were found dead around midday on Wednesday, one in the northeastern town of Arta and another at S'illot further south on the coast.
He said: "My solidarity and support goes out to the families and friends of victims and all the affected by these tragic floods", he said. "We had to swim to try to survive".
Tennis star and local lad Rafa Nadal helps in the clean-up efforts.More news: HMD Global launches Nokia 3.1 Plus and Nokia 8110 4G in India
Emergency services in the Balearic archipelago tweeted that the death toll had risen to 10 and a little boy remained missing.
Officials have said more than 600 rescuers and medical staff were at work and that emergency relief centres had been set up in sports halls.
At least three towns closed schools and hundreds of people were sheltered in sport facilities and a local horse racing track.
"What is most urgent right now is to find missing people and address the concerns of their relatives and all neighbours", Prime Minister Pedro Sanchez said during a visit to the disaster zone.More news: Google is extending Home Control from this week
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