The National Enquirer won’t let up on the gay rumors surrounding Jessica Simpson’s dad, Joe Simpson.

First they claimed that Joe was sugar daddy to a 21-year-old boy toy by the name of Bryce Chandler Hill. Bryce vehemently denies the rumors.

Now the tabloid is alleging that Jessica’s dad hired a male escort for $600 at a swanky hotel in New York.  The escort, Joey Anderson, even passed a lie detector test. Joey told the tabloid, “We rolled around, kissed and gave each other oral. He seemed to have an insatiable appetite for sex and never appeared tired.”

RumorFix has reached out to Papa Simpson and his reps for comment. But so far no word.

We’ve also learned exclusively that escort Joey Anderson is still advertising his services on a website called “Hour Boy.”

The escort, who is really 32, lies about his age saying he’s 25 and offers body rubs, massages and travels internationally.

He specializes in “foot play.”  Joey’s ad claims he has “an angelic face, boyish w. long hair, masculine, fit, and smooth. Educated and can hold a convers. I am fully versatile, can be dom/rough or passionate and affectionate.”

His fees range from $225 to $2,500.

The Simpsons haven’t commented on the persistent rumors except to make this announcement when Joe and his wife of 34 years, Tina announced their divorce:

“It is an amicable split and there is no third party involved. Any other related allegations are completely false.”