One of the people who could be the extortionist behind the Kevin Hart sexually explicit video contacted his lawyer and offered to take a lie detector test ... but the comedian would have to write a huge check to make that happen.

Sources familiar with the case tell TMZ ... the bizarre call was made recently by a person who apparently has some connection to the encounter between Kevin and the woman pictured above.

The person who called Hart's lawyer did not say what they would answer while hooked up to the polygraph, but said they would only sit for a 6-figure amount -- we're told somewhere around $500,000.

The crazy thing is this ... if the person is the extortionist, they're essentially saying they would go to prison for $500k. If they're not the extortionist, then they're a scam artist. 

Our sources say Kevin's attorney did not bite. 

As we reported, the FBI is on the case and is honing in on a suspect