The two women accusing George Foreman of sexual abuse 45 years ago -- when they were minors -- want to hook him up to a polygraph ... challenging him to a lie detector test.
The boxer's alleged victims, Gwen Hunter and Denise Shipes, say George made them out to be liars and villains when he countersued them and accused them of extortion ... and they say they passed their own lie detector tests.
The accusers' attorney, Samuel Dordulian, tells TMZ ... Hunter and Shipes took their polygraph tests with one of the world's preeminent experts in the field, an examiner they believe George's legal team has routinely used for past cases, and they want Foreman to use the same person.
TMZ broke the story ... the women sued George back in August, claiming the pugilist was in his 20s when he groomed, and eventually sexually abused them when they were still underage. They say it all happened in the late 1960s and early 1970s.
Hunter detailed her allegations in a news conference three months after filing suit, saying ... "He asked me to remove my clothes, and if I didn't then my father would be fired, so I complied."
As we first reported ... George then filed a countersuit against Hunter, claiming she was intentionally dragging his name through the mud and flat-out lying to score a payday.
The accusers say they wanted to clear their names after George's countersuit, and they claim their lie detector tests show they're telling the truth ... and now they want Foreman to take one.
What's more, their attorney tells us he's in the process of bringing a separate defamation countersuit against George in response to what they say are baseless and harmful claims of extortion.
The timing of this all is worth noting ... in a few weeks, the "Big George Foreman" biopic is set for release.
We reached out to Foreman's reps ... so far, no word back.