A new YouGov poll of 1,130 people found that 57 per cent of Corbyn supporters want the new Labour leader to follow the Conservatives in their support of the EU, though this was less than supporters of the other three leadership candidates.
Only seven per cent of Corbyn voters want him to campaign for a Brexit.
The poll, conducted last week, also found 74 per cent of Corbyn's supporters want the UK to remain a member, while just 14 per cent want the UK to leave, and 11 per cent do not know.
Of those eligible to vote in the Labour party leadership election, the results showed 77 per cent would vote to remain a member of the EU – including those who voted for Corbyn.
This comes after dividing lines have already been drawn by members of the shadow cabinet on the European Union question, with some new shadow ministers pledging to resign if Corbyn’s front bench had to campaign to leave.
Unions have also rallied to warn they could also campaign to leave the EU if the government jeopardises workers rights.
However, inside Westminster, yesterday Lord Falconer, a Blairite who has taken the position of shadow justice minister, said he would resign if Labour backs the EU exit.
On the back benches, Phil Wilson, MP for Sedgefield who co-chairs a pro-EU group of Labour MPs, insisted up to 100 Labour MPs would rebel against Corbyn if he toed the union line, and would push for the UK to stay in the EU.
The results of the poll come three days after Corbyn hailed a new mandate given by his supporters, putting pressure on him to respect his voters' views on the EU.
Alan Johnson, the former Labour home secretary who is leading the party’s EU referendum campaign, is due meet Corbyn for talks on the issue later this week.