Sunai Manomaiudom, director-general of the DSI, Thailand's equivalent of America's FBI, said: "We will give everyone an equal opportunity by extending the deadline for one month.
"If they fail to show up, we will conclude the case and request arrest warrants."
Noppadol Pattama, Thaksin's lawyer, said on Tuesday that his client will not return until after an election expected to be held in December.
He said that the country is ruled by the military who gained power by undemocratic means and the investigations targeting Thaksin are unfair.
Thaksin also fears for his safety, said Noppadol. Thaksin's wife Pojamarn lives in Thailand and can travel abroad freely.
She is currently in Singapore from where she has filed a formal request for a delay in her appearance on medical grounds.
According to the DSI, Thaksin and other family members controlled nearly 80 per cent of SC Asset - a Shinawatra family real estate company - both directly and through nominee companies, and sold their interests to outside parties last year.
The charges that Thaksin and his wife face for allegedly violating exchange regulations carry a maximum penalty of two years in prison and a fine of $15,500.
The military deposed Thaksin after lengthy street protests accusing him of corruption and abuse of power.
One of the coup leaders' first acts was to initiate corruption probes against Thaksin.