It comes as the party started sending ballots to its half a million members, registered supporters and affiliates on Monday before the next leader is unveiled at a special conference on 4 April.
According to the survey by YouGov, the shadow Brexit secretary has a convincing lead over his rivals Rebecca Long-Bailey and Lisa Nandy and could win the support of 53 per cent of members’ first preference votes.
Ms Long-Bailey, the candidate most closely associated with Mr Corbyn’s left-wing policy agenda, would emerge with 31 per cent while Lisa Nandy, the MP for Wigan, could win 16 per cent of first preference votes, according to the survey.
Under Labour’s preferential voting system, if a candidate wins 50 per cent of the votes on the first round, they win the contest outright.
Earlier on Wednesday, the shadow Brexit secretary won the endorsement of the London mayor, Sadiq Khan, claiming he was the “best person to unite” Labour and put the party in government for the first time in over a decade.
Jenny Chapman, a former Labour MP who is chairing Sir Keir’s campaign for the leadership, described the polling results as “encouraging”.
Among members of the left-wing group Momentum – set up to support Mr Corbyn’s policy agenda – 71 per cent of those questioned said they would back Ms Long-Bailey, while 19 per cent opted for Sir Keir and 10 per cent for Ms Nandy.
The survey also showed Angela Rayner, the education secretary, ahead of the other candidates in the deputy leadership by a significant margin. She could win 47 per cent of first preference votes while her closest competitor, Richard Burgon, may win the support of 19 per cent of members.
The poll was commissioned by Sky News and surveyed 1,323 Labour members between 20 and 25 February.