Twitter IPO home still in flux, no decision on NYSE: Sources

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Not so fast, New York Stock Exchange.

Despite a report that Twitter had chosen to list its initial public offering on the NYSE, sources tell CNBC that Twitter is only leaning toward the Big Board, and that no final decision has yet been made.

(Read more: Cramer: Twitter IPO will be a 'circus')

Although representatives of the NYSE went calling on the microblogging site's San Francisco headquarters recently, sources familiar with Twitter's thinking say the conversation is ongoing. That would mean that a possible listing on the Nasdaq Stock Market remains in play.

Yet the mere suggestion of Twitter—one of the marquee names in technology—making its home at the NYSE may sting. While the Nasdaq is the destination of choice for most tech listings, including Facebook, the market has grappled with a string of high-profile blunders.

Facebook's 2012 IPO was widely considered to have been mishandled, and resulted in the Nasdaq being sued. Meanwhile, a massive outage last month left the stock market red-faced, and is still shrouded in controversy.

--Reporting by CNBC's Julia Boorstin; writing by Javier E. David