Pita Limjaroenrat of the Move Forward Party (MFP) will likely receive fewer than five votes from the Senate in the parliamentary election for the new prime minister, according to a senator.
Mr Pita will struggle to draw five or more votes from the 250 senators during the vote, senator Kittisak Rattanawaraha said on Wednesday.
Most of the coup-appointed senators seem to have decided they will either vote against Mr Pita or abstain, he added.
The senator said he suspects Mr Pita may not be the only candidate entering the race.
The vote is expected on July 13.
Any party that has won 25 House seats or more can nominate up to three candidates.
The MFP has vowed to press for an amendment to Section 112 of the Criminal Code, or the lese majeste law. This is believed to be the prime reason why many senators will not back Mr Pita in his bid to become prime minister.
Mr Kittisak said political unrest is likely, no matter who becomes the new leader of the country.
Mr Pita claimed on Tuesday that he had enough support in the Senate to ensure his election as prime minister.
He said he hoped the Senate would not go against the people's wishes.