I don't know where that twitter user has got his information from; I can't find any confirmation in the German media, on BVB's website or Dortmund forums. Latest information is that the decision is still to be made, Bild is even reporting today that he's considering moving to England, while Focus reports that Tuchel has apparently made a decision in favor of Bürki.
I'd be very surprised if the tweet information is true. If anything, Weidenfeller's errors could prove much more costly in the Europa League or in the DFB cup knock-out games, where there isn't even a 2nd leg to make up for blunders.
E: Looks like Sport1 is the source the twitter user is referring to. They say it's "according to their own information". So better take it as gossip; they've been unreliable even when it comes to Bayern and I don't know they have any notable connections to the Dortmund camp.
"Now, here, you see, it takes all the running you can do, to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that!" - Red Queen, Alice - Through the Looking-Glass