If Facebook and Nasdaq were in a relationship, the status would likely read: “it’s complicated.”

The relationship was on a rocky road from the start. The Nasdaq exchange, home to many tech stocks, had an unplanned 30-minute delay in offering Facebook stock on its IPO day, which may have contributed to the stock’s meager performance.

Nasdaq declared itself “embarrassed” by the glitch, and earmarked $13 million to cover “bad trades” made by investors whose schedules were thrown off.

But that face-saving gesture may not have been enough for Facebook. According to a Reuters source, the social network is mulling a breakup with Nasdaq — and a hook-up with the New York Stock Exchange.

The report says Facebook sat through a pitch from the NYSE, and is mulling the option to switch its official listing exchange.

In a statement to Bloomberg, however, a NYSE representative indicated reports it was in talks with the social network are false. They’re just good friends.

“There have been no discussions with Facebook regarding switching their listing in light of the events of the last week nor do we think a discussion along those lines would be appropriate at this time,” the rep said.

No further comment was offered by Facebook or Nasdaq.

Although unusual, such a move would not be entirely unprecedented. Viacom went in the other direction recently, switching from the NYSE to Nasdaq to save fees in November 2011.

Should Facebook consider switching exchanges so early, or dance with the one who brung it for a while longer? Let us know your take in the comments.