Floyd Mayweather -- Deal with Berto Not Done ... Yet

Andre Berto has NOT signed on the dotted line to fight Floyd Mayweather on September 12th ... but they're getting there ... sources connected to the deal tell TMZ Sports.

As we previously reported, Mayweather dropped Berto's name as a possible opponent -- and Berto WANTS to fight Floyd -- but the fact of the matter is the deal has not been finalized.

Our sources tell us ... the two sides have spoken -- but without a firm deal in place, we're told Mayweather's camp is still reaching out to other potential opponents in case Berto falls through.

That being said, our sources tell us it's pretty likely the two sides WILL come to an agreement -- this isn't at all like the Pacquiao situation which took FOREVER to close.

We're told there should be some significant movement in the next few days.