Although R. Kelly's camp has been referring to the unpaid $32k as "interest" ... our sources connected to the case say that's not entirely true.

We're told only $11,500 of that amount is interest, and the rest -- about $20,800 -- is for unpaid child support and educational and healtcare expenses for the children.

Kelly's attorney, Steven Greenberg acknowledges, "Yes, he owes for some some educational and healthcare expenses that aren't documented -- and, I question if they're even true -- and some interest.

He also says Kelly intends to "pay the money whether he agrees with it or not at this point."

R. Kelly is on the hook for another significant child support payment ... and his ex-wife wants to set a firm deadline to get the dough, because she's convinced he'll never pony up otherwise.

According to new legal docs obtained by TMZ ... the disgraced singer's ex-wife, Drea Kelly, is asking the court for a hard and fast deadline for Kelly to pay her the $32k he owes in interest on back child support.

In the docs, Drea claims Kelly is dragging his feet on the payment because the court never imposed a set date for him to cough it up ... and she wants a deadline to be enforced, or else she thinks she'll never see the money.

Remember, Kelly's been required to pay $20,833 per month in child support since January 2009. He fell behind on his payments, to the tune of $161,633, and was arrested and sat in jail until he paid his tab.

But, Drea's still fighting for the interest on that money ... and she wants the court to get involved to force Kelly's hand. Kelly's crisis manager, Darrell Johnson, says they are aware of the pleading and will respond accordingly.