Neither political leader is winning over voters but Tony Abbott and Bill Shorten are neck and neck in the popularity race, a new poll shows.

Just 13 per cent of voters interviewed in the latest Morgan Poll prefer Mr Abbott as prime minister, while 12 per cent believe Mr Shorten is the right man for Labor's top job.

Mr Shorten has taken a fall in the latest poll - nine per cent of voters have abandoned him as their preferred leader since April.

This follows his being summoned to the witness box at the royal commission on trade unions and the revelation of an undeclared $40,000 campaign donation.

His leadership will be under the microscope over the next few days as he faces at least one internal fight over his backflip to support a policy of turning back asylum-seeker boats.

Voters would rather see deputy Labor leader Tanya Plibersek (26 per cent) or Anthony Albanese (19 per cent) take the opposition's reins, according to the survey.

Mr Abbott has improved his popularity by one per cent since April but is yet to reach the levels he attained in the weeks before he survived a spill motion, when 14 per cent of voters wanted him as prime minister."