The visit will take place towards the end of April, around two months before the June 23 referendum in which Britain will decide whether to leave or stay in the 28-country bloc, The Independent on Sunday said.
A spokesman for Prime Minister David Cameron's Downing Street office refused to comment on the report, calling it "speculation".
Obama is heading to Germany in late April to talk trade with Chancellor Angela Merkel and promote US exports at the Hannover fair, said to be the world's largest for industrial technology, which takes place April 25 and 29.
Washington has long backed Britain playing a central role in the world's largest economic bloc, warning the "special relationship" with the UK could be at risk if Britain were to leave.
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Leave.EU, one of the campaign groups calling for Britain to pull out of the EU, blasted the reported plans for intervention by Obama.
"People in this country have had enough of American presidents dictating our foreign policy to us," said the campaign's spokesman Jack Montgomery.
Cameron favours keeping Britain in the EU, following a renegotiation of the UK's relations with Brussels.
Opinion polls indicate that the race is finely balanced, with those who want to remain at 51 per cent and those in favour of leaving at 49 per cent, according to a poll of polls by the What UK Thinks research project.