The study also projects massive losses for the ruling Congress in Delhi and says AAP's Arvind Kejriwal is the most preferred choice for chief minister.
The survey says the Bharatiya Janata Party (BJP) is likely to secure 33 per cent vote share in Delhi, while AAP is expected to secure 27 per cent vote share and the Congress would finish third with only 23 per cent vote share.
It said that AAP may get between 13 and 21 seats in the 70-member assembly and the Congress may get between nine and 17 seats.
According to its study, released to the media, 70 per cent of respondents say that the Sheila Dikshit government does not deserve another chance at governing Delhi, while only 23 per cent of those surveyed want the Dikshit government to get another chance.
The post-poll survey suggests that the satisfaction levels with the Dikshit government has dropped by 26 per cent from the 2008 mark of 66 per cent.
Only 40 per cent respondents say they are satisfied with the Delhi government's performance in the past five years while 54 per cent said they were dissatisfied.
The Delhi chief minister's personal popularity has also touched its lowest since 2003, the survey said. She got only 15 per cent approval.
Dikshit's popularity ratings in 2008 stood at 34 per cent and climbed to 41 per cent in 2009, the survey said.
Kejriwal emerges as most preferred choice for chief minister of Delhi at 27 per cent, followed by BJP's Harsh Vardhan at 22 per cent approval. Dikshit is third at only 15 per cent.
The post-poll projects Dikhshit may lose New Delhi seat to Kejriwal. It says 38 per cent respondents in New Delhi constituency say they want Kejriwal as chief minister, while only 13 per cent back her.
The post-poll projections suggest Dikshit may be paying a price of the "high unpopularity of the Central government" as 63 per cent Delhi respondents say they are dissatisfied with the Congress-led United Progressive Alliance government.
Among the reasons given by those who voted for thed BJP was they are attached to the party and the price rise, while those who voted for AAP said they wanted change. Congress voters voted for it due to family loyalty.
Kejriwal was also the most preferred choice of young voters, while Harsh Vardhan was the preferred choice of Brahmins, and Muslims voted for Dikshit.
BJP approaching AAP candidates?
Unconfirmed reports by Times Now says that BJP is secretely meeting AAP candidates ahead of the results day. Many top BJP leaders have already admitted that the party is unlikely to get a majority in the state.
Meanwhile, AAP will not get into alliance with the BJP, said its leaders on Friday.
"There is no question of supporting either the Congress or the BJP. Our votes are because of the anti-establishment stand that we have. If we ally with any of them what kind of credibility will we have," said AAP member Yogendra Yadav.
(With IANS inputs)