Salehi is being protected by Karzai allegedly because he knows too much about the inner workings of the presidential palace, including details of widespread corruption, an Afghan politician told the Times.
Police arrested Salehi during an investigation into New Ansari, a money transfer firm that relies on couriers and other low-technology methods to move cash into and out of Afghanistan.
Since the US invasion of Afghanistan in 2001, New Ansari has grown into a financial hub in Afghanistan, moving billions out of the country, mostly to Dubai, for "wealthy Afghans of every sort" including politicians, drug traffickers and anti-government fighters, The New York Times reported.
Salehi is allegedly a confidant of some of the most powerful people in the Afghan government, including Engineer Ibrahim Spinzada who was, until recently, the deputy chief of the Afghan intelligence service.
The CIA declined to comment on allegations that it paid Salehi.
Allegations of corruption and nepotism have dogged the US presence in Afghanistan and such problems undermine support for Karzai's government and foreign nation-building efforts, analysts say.