Now that Sting is in the TNA HOF will he ever be in the WWE?

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Sting is most known for his work in WCW, and since WWE owns WCW and all its archive footage, wouldn't it be a fair assumption that Sting be inducted into the WWE Hall of Fame one day? But now that he is the first inductee into the TNA Hall of fame, is this still likely to happen? I mean the WWE inducted ric flair into the hall of fame twice, so why not sting, even tho he is part of the TNA hall of fame. He played just as big of a part in WCW as TNA, if not bigger. Vince McMahon probably wont want to induct him because he refused to come to WWE after WCW went under. I have herd that he can be very petty. I guess time will tell. They will probably just continue to induct people who dont deserve it or that know one has ever herd of. I think AJ Styles should be the second inductee into the TNA HOF and that could aid in their current storyline with him dixie and surge.