The coup has split the Pheu Thai Party into differing groups, with former premier Thaksin Shinawatra not keen on forming a government-in-exile, a highly placed source in the former ruling party said on Friday.
Some members have openly said they will fight the National Council for Peace and Order (NCPO) while others have opted not to resist the coup-makers and keep a low profile.
A third group has decided to wait and see how the political situation unfolds before they react.
The source said the anti-coup group's most vocal member is fugitive red-shirt leader Jakrapob Penkair, who is reportedly manoeuvring to set up a government-in-exile.
The government-in-exile idea was put to Thaksin, who disagreed.
The ousted premier thought the time was not right to play the government-in-exile card, seeing that many people still support the coup and reactions from foreign countries to the military takeover were not strong enough to apply pressure on the junta.
Also, being seen to openly embrace a government-in-exile could seriously harm the Shinawatra family's political and business interests. The coup-makers have the use of martial law which could easily lead to swift prosecutions.
However, Mr Jakrapob has not given up on establishing an administration abroad although instead of calling it a government, he might name it an organisation-in-exile.
Meanwhile, several core red-shirt members have talked of a neighbouring country allowing an overseas anti-coup group to launch an anti-junta movement from there.
The source said Mr Jakrapob has frequently travelled in and out of the unnamed country of late.
He is thought to have met with key Pheu Thai Party members, who reportedly fled the country after the coup on May 22.
The group plans to operate from this neighbouring country to try and spread anti-coup sentiment in Thailand and encourage the international community to apply more pressure on the junta.
The source said the "wait-and-see" group of politicians and businessmen, including those called by the NCPO to report in earlier, is now gauging anti-coup sentiment on social media networks and among people upcountry.
As for the "non-resistance" group, these members feel they have no choice but to lie low because they are bound by agreements signed with the NCPO not to aid a political movement or face prosecution and have their assets frozen.
The source said these members were afraid of being deprived of their financial freedom.
Probes of their assets, if ordered, could lead to their tax records and other transactions being scrutinised, a step which could result in asset seizures, the source said.