Paetongtarn Shinawatra's support jumped 10 points to 38.2 per cent in a survey conducted by the National Institute of Development Administration (NIDA) published at the weekend, while Prayut trailed in third place with 15.65 per cent.
Opposition politician Pita Limjaroenrat, who heads the Move Forward party, received support from 15.75 per cent of respondents.
Thailand is expected to hold an election in May, which will continue a long-running political battle between the Shinawatra family and the conservative pro-military establishment.
Thailand's Royal Gazette would announce the dissolution of parliament later on Monday, Deputy Prime Minster Wissanu Krea-ngam said.Â
An election must take place within 45 to 60 days of dissolution.
Prayut, who has been in power since staging a coup against the last Shinawatra government in 2014, shrugged off the latest survey result.
"Poll is a poll. It depends on what the people want ... it should not damage the country - that is most important for the next government," Prayut told reporters on Monday.
"I want to do my best," he said.
Paetongtarn, 36, better known locally by her nickname "Ung Ing" is one of the nominees for prime minister for the Pheu Thai party, which together with its previous incarnations has won every Thai election since 2001.
The NIDA Poll, which surveyed 2000 voters across Thailand in March, also showed almost 50 per cent of respondents said they would back parliamentary candidates from Pheu Thai.
Paetongtarn on Friday said she was confident of winning the election by a landslide, with the aim of averting any political manoeuvring against her party, which has previously been removed from office by judicial rulings and military coups.
