Students and housewives could also be used as part of the reported scheme to tackle fraud, which could include hidden cameras and recording devices.
It is said to be one of the ideas Greece will raise at a meeting of eurozone finance ministers on March 9.
Greece needs to convince them it is serious about reform to receive further credit.
Eurozone leaders want to extend help on Greece’s €240 billion ($272 billion) bailout until the end of June in return for commitments to further reform.
The leaked document, a letter reportedly sent by Greek Finance Minister Yanis Varoufakis to Eurogroup president Jeroen Dijsselbloem, was seen by the Financial Times and AFP.
“The culture of tax avoidance runs deep within Greek society,” the letter reportedly says.
“Tax authorities are not only understaffed but immersed in the logic of book-checking when the real problem lies off the books.”
Informal tax inspectors would be hired on a “strictly short-term casual basis – no longer than two months and without any prospect of being rehired”.
Yanis Varoufakis is quoted as saying that the very news that there were thousands of casual onlookers carrying spying equipment on behalf of the tax authorities could shift attitudes quickly.
The amateur inspectors would be able to go to places traditional tax inspectors would be wary of visiting such as nightclubs and medical facilities, he added.
Other proposals reportedly include taxing online gambling, streamlining the bureaucracy and activating an existing plan for an independent watchdog to monitor government fiscal policy.
The new government also wants to spend more money to help those who have been hardest hit by Greece’s long recession.
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