There's talk that the probe could be settled without the results of the investigation being made public.
But it would likely be an explosive case should it see the light of day.
Market manipulation has been a central focus of the FMA since its establishment in 2011.
Its case against Diligent Board Member Services founder Brian Henry, launched in 2013, was the first brought in New Zealand.
Henry admitted to market manipulation last year and was ordered to pay a $130,000 penalty after settling with the FMA.
And last month the market watchdog issued a warning to an "inexperienced" online trader, who wasn't named, over suspected manipulative trading.
In the 12 months to June 30 last year the regulator had received three referrals or complaints about market manipulation from exchange operator NZX and members of the public, according to its 2014 Investigations and Enforcement report.
Asked for update on the number of market manipulation investigations presently underway, an FMA spokesman said: "We don't generally comment on numbers in between the statutory annual reports."