Even as he sits in jail awaiting trial for murdering his ex-wife, former Illinois cop DREW PETERSON is on the prowl for women!

In a dozen jailhouse love letters obtained exclusively by The ENQUIRER, Peterson – a prime suspect in the disappear­ance of his fourth wife Stacy – repeatedly propositions 40-year-old Diana Grandel.

The 57-year-old former police sergeant from Bolingbrook, Ill., asks for the single mother of two’s measurements, begs for a photo of her in a bikini, wants to know if she has any sexually transmitted diseases and describes what he wants to do with her in bed.

“I just think of your smile and holding you in the dark feel­ing your body against mine…I want to spend a lot of time with my lips on yours,” the ac­cused killer states in one letter.

In another, he tells Diana he likes “sex with a lot of foreplay…I’m more into pleasing my partner than myself.”

Even more shocking, Peterson – sticking to his story that Stacy walked out on him – tells Diana that she can have all of his missing wife’s clothes.

Diana – who has known Peterson since she was a young teen – was stunned when he offered her Stacy’s wardrobe, telling The ENQUIRER: “That’s when I realized that Drew had probably killed Stacy."

When Stacy Peterson disappeared on Oct. 28, 2007, Drew was thrust into the national spotlight because of suspicion he had killed her and disposed of her body.

Authorities then reopened the investigation into the March 2004 death of his third wife Kathleen Savio.

Investigators initially classified the case as an accident, saying Kathleen drowned after she fell in the bathtub.

But it was reclassified a homicide and Peterson, who earned a reputa­tion for clowning around with report­ers, was indicted and arrested on May 7, 2009, for Kathleen’s murder. He’s been sitting in the Will County jail ever since, awaiting trial.

 Stacy’s body has never been found.

All the shocking details are in the new ENQUIRER – ON SALE NOW!