Members of the so-called House No 111, or former executives of the defunct Thai Rak Thai Party, have never pressed for a cabinet seat, Varathep Rattanakorn said on Monday.
Mr Varathep, one of the 111 whose five-year political ban has just expired, was a former deputy finance minister in the Thaksin government.
He dismissed as a rumour the report which had been spread around for some time that he and some other members of House No.111 had pressured Prime Minister Yingluck Shinawatra for cabinet posts.
Some of the surviving and active 111 had already been assisting the government in different fields, he said.
Mr Varathep said he had never been approached to join the cabinet. He had never asked for a cabinet post but was willing to help the government in any position.
Phumtham Wechayachai, the Pheu Thai Party director, also denied the report.
Both Mr Varathep and Mr Phumtham said the prime minister had the sole power to decide when to reshuffle the cabinet and who to join it or be left out.
Mr Phumtham asked all not to speculate that he would take the post of interior minister.
Weng Tojirakarn, a Pheu Thai Party list MP and leading member of the United Front for Democracy against Dictatorship (UDD), said that in his opinion the party should consider appointing Jatuporn Prompan, a UDD leader, to a cabinet post since he had long worked for the party.
He said both Natthawut Saikuar, the current deputy agriculture minister, and Mr Jatuporn had the qualifications for a cabinet post.
Chartthaipattana Party leader Chumpol Silpa-archa, the deputy prime minister and minister of tourism and sports, said Ms Yingluck had so far not sent any signal about a cabinet reshuffle.
Yongyuth Wichaidit had left only two cabinet posts - deputy prime minister and interior minister - vacant and other ministers could be assigned to take charge of his responsibilities.
The prime minister would decide when to reshuffle the cabinet, Mr Chumpol said.