Our real estate sources tell us Bing's former mansion in Rancho Mirage, CA is up for sale at $4.5 million ... and the place includes a guest house dubbed the "JFK Wing."

The sprawling estate is 6,700 square feet with 5 bedrooms ... sitting on 1.36 acres in the esteemed Thunderbird Heights neighborhood in the desert town near Palm Springs.

The place features panoramic views of the surrounding mountains and valleys ... and it's got all the bells and whistles, including theater room, pool and spa, bar, putting green and an outdoor kitchen.

The master suite is 1,400 square feet and comes decked out with a fireplace, walk-in closet and tub, plus indoor and outdoor showers.

The guest house, where JFK often stayed, is on the opposite side of the residence ... and it features 2 bedrooms and 2 bathrooms, plus a full kitchen and living room.

As you probably know, JFK had a well-documented affair with Marilyn, and they found places to meet ... one of which was Bing's pad.

The neighborhood is super private with high-level, 24-hour security ... so it's no wonder the place hosted celebs like JFK and MM, and was home to Bing.