Protesters have accused Thaksin, who was ousted in a bloodless coup in 2006, of continuing to pull the government's strings remotely from exile in Britain.
Kudeb Saikrachang, a spokesman for the PPP, has admitted that Thaksin "still has a lot of influence".
"He gives advice to people within the party and they listen," he said.
On Tuesday, Thailand's Supreme Court issued a second arrest warrant for Thaksin when he failed to appear in court to acknowledge charges against him in one of four pending corruption cases.
A first warrant was issued after he fled the country in July in connection with a separate case.
The rebel MPs – 73 out of the PPP's 233 legislators in parliament – say appointing a Thaksin relative would only inflame and prolong anti-government protests.
|Critics accuse Thaksin of continuing to pull the government's strings from exile [EPA]
They stormed out of a party meeting on Monday when their call to hold an open debate on potential candidates was rejected, and they have signed a petition asking the party to reconsider Somchai's nomination.
The group has also threatened not to back the party's choice when parliament meets on Wednesday.
Boonsong Wongtrirat, a spokesman for the rebel MPs, said they would "abstain from voting if [Somchai] is formally nominated".
"We want to choose a candidate who will not aggravate problems … a candidate for the prime minister should not be a controversial figure," he said.
Protesters are not clear about who they want in government but they know who they do not want: anyone connected to Thaksin.
The People's Alliance for Democracy which has been leading the protests, had earlier claimed only to be seeking Samak's resignation, but it has now rejected anyone from the PPP and has vowed to continue its campaign if Somchai is made leader.
Chamlong Srimuang, one of the protest leaders, said Somchai would "be even more [Thaksin's] proxy than Samak ever was".
Some party members have suggested that dissolving parliament to force new elections is the only way to resolve the dispute.
Party sources say Somchai's wife and Thaksin's sister, Yaowapha Wongsawat, even warned the MPs on Monday to support Somchai or face parliament being dissolved - and them losing their seats – but Somchai ruled that out on Tuesday.