Mr Preesa said police searched the room in the guest house where Grainger was staying and found about a gram.
He said it was possible Grainger was overstaying as police also found a passport that had expired two years ago, despite Grainger telling them he had an updated passport.
A staff member at the Phuket Wan news site said police probably wanted Grainger to pay up front to avoid being charged but the cost would have been "a substantial donation".
The person said conditions in Phuket Prison where Grainger would likely be staying were horrific. "It's built for 750 people and there are more than 3000 in there. Prisoners can't lie on their backs, they have to lie on their sides because it is so crowded. It's pretty awful."
If Grainger does go to Phuket Prison he'll be in the company of New Zealander Garry Halpin, who this year admitted charges of dealing in crystal methamphetamine, or P, to teenagers in Phuket.
Halpin was jailed for four years and 10 months and fined 250,000 baht ($9816) after police found more than 18g of P, drug paraphernalia and a digital scale. The former Phuket tourist police volunteer's sentence would have been doubled had he not pleaded guilty.
According to Thailawforum.com, possession of yaba, the form of P Grainger was caught with, can result in one to 10 years in prison and/or a fine of up to 200,000 baht.
Those found with more than 20g of yaba can face intent-to-sell penalties, the most severe of which is death.
Grainger's arrest follows those of two other Kiwis, both of whom are in prisons in Bali and China.
Antony de Malmanche, a 52-year-old sickness beneficiary from Wanganui, was arrested at Bali's Denpasar airport, allegedly with 1.7kg of P in his backpack on December 1. Peter Gardner, 25, was detained in China in November and could face execution by firing squad after two items of his luggage checked in to a flight from Guangzhou to Sydney were found to contain 30kg of P.
Mfat said staff in both countries are providing consular advice.
