Burger King Makes Offer On Elvis Presley House -- It Could Be Our Greaseland!

The home of The King .. could become the home of the Whopper ... 'cause TMZ has learned the honchos at BK have made a serious offer on Elvis Presley's former Bev Hills home.

TMZ obtained a letter from Burger King Corp. to Peter Morton -- who owns the 5,367 square foot Elvis Presley Estate in the 90210 -- which states the company's intention to buy the house for a cool $3.69 mil.

The letter reads, "This would be a fast closing within three days and we would be happy to provide you with proof of funds upon request."

BK says if Morton agrees to the sale, the company will "preserve all residential historical value."

Buuuut, there are a few problems -- first, the house isn't really on the market.

Second, Morton bought the house back in December for $9.8 mil ... and there's virtually no chance he's willing to take a $6 million hit on the place.

Sidenote -- the timing of the offer is interesting, 'cause it happens to coincide with the launch of BK's new sandwich, the Big King (Big King ... King of Rock 'n Roll ... we get it).

BK wants to move fast -- really fast. In fact, BK's put a ticking clock on the offer ... it ends at midnight TONIGHT.