9:50 AM PT -- A source connected to J Lo tells us 'WoD' was floating around NBC years ago -- it was the network's concept and they brought it to Jennifer.

Jennifer Lopez pulled a sneaky 1-2 step to get her hit TV show, "World of Dance," on the air ... at least according to a guy who claims she stole the idea -- but his story's got some holes.

Alvin Gray-El is suing J Lo claiming 'WoD' is a total rip from an idea he first pitched to renowned choreographer Debbie Allen. In docs, obtained by TMZ, Alvin claims he faxed Debbie a copy of his idea back in 2009. His reality show was supposed to be entitled, "Let's Start the Dance."

Alvin, however, says he never heard back from Debbie, whom he's also suing.

The following year, according to docs, Alvin registered his show idea with the U.S. Copyright Office -- but was told about 7 years later ... there was already a similar show being produced by J Lo and NBC.

Alvin claims he fired off a letter to NBC telling them the show J Lo's producing is his original pitch from years ago he made to Debbie. But, he says he got zero response.

BTW, Debbie has nothing to do with J Lo's show. Assuming she actually got Alvin's fax all those years ago, Alvin's lawsuit never explains how his idea jumped from Debbie to Jennifer.

In any event, he's now suing both of them for $6.5 million in damages. We've reached out to J Lo's camp and Debbie's ... so far no word back.