Business support for membership of the EU has narrowed from 74% six months ago to 62%, according to a survey of large businesses by consultants Deloitte.
The majority still say the UK is better off in the EU, but the number backing moves to leave has risen from 2% to 6%.
But research from Britain Stronger in Europe suggested £236bn of UK exports, which is about 80% of the total, would be at risk if Britain left the EU.
An in-out referendum on the UK's EU membership is due by the end of 2017.
Deloitte surveyed 137 chief financial officers (CFOs) of FTSE 350 and other large private companies, including 24 CFOs from the top 100 companies, between 11 November and 2 December 2015.
In total, 28% of those who were surveyed said their decision depended on the outcome of the renegotiation of UK membership, up from 23% in the second quarter of last year.
The final 4% are uncertain of their position, up from 1% in the middle of last year, meaning the total of "don't knows"' and those whose decision will depend on the results of the renegotiation has risen to 32% of all CFOs, up from 24% in the second quarter.
Ian Stewart, chief economist at Deloitte, told the BBC that the results of the survey suggested the outcome of the Prime Minister's renegotiation with European leaders could have an effect on how people voted in the referendum.
"It suggests there is a hope that the renegotiation will deliver material improvements for the UK and a sizeable majority are waiting to see.
"The backdrop of a continued weak recovery in Europe, the migrant crisis and continued uncertainties over the structure of the monetary union means public opinion has [become] more negative and we've seen a similar shift among chief financial officers."
The Britain Stronger in Europe pressure group says that the EU accounts for half of UK goods exports, worth £148bn in 2014, and that trade would be put at risk by leaving the EU.
It says that taking into account deals currently being negotiated by the EU takes that figure to 80%, which brings the total to £236bn.
"If we leave, those exports would be at risk, facing trade barriers and fees - hitting British businesses hard and increasing prices in the shops," said Stuart Rose, chairman of the Stronger In campaign.
"These are the stakes. Those proposing leaving the EU must show how this damage can be avoided."
Robert Oulds, director of the Bruges Group, a Eurosceptic think-tank whose founding president was Margaret Thatcher, said the Deloitte survey was significant: "Business leaders are beginning to think outside of the box and recognise that we do not have to be part of an EU political union to enjoy mutually beneficial trade links.
"If this trend continues then businesses will be firmly in favour of 'Brexit'."
Will Straw, executive director of Britain Stronger In Europe, the umbrella organisation lobbying to stay as part of the EU, said the result still showed a clear preference from business for the status quo: "An overwhelming majority of business leaders think Britain is stronger and better off in Europe. Just 6% think it would be better to leave.
"Being part of the largest market in the world allows Britain's economy to thrive, supporting jobs across the country and lower prices in the shops. Leaving Europe would put all that at risk, which even Leave campaigners admit would cause economic 'pain' to Britain."
The Deloitte survey also asked financial officers for their views on the direction of the economy in 2016.
It found that businesses' attitude to risk had slipped and business confidence had fallen back to 2012 levels.
Only 12% said they were more optimistic than three months ago, down from 36% six months ago.
Expectations for inflation was fairly split, with 51% of CFOs expecting inflation to remain below 1.5% in two years' time and 44% expecting it to be between 1.6% and 2.5%.
On interest rates, those surveyed seemed well prepared for a move upwards, with 64% saying they could withstand a rise in rates of one percentage point to 1.5% before they would need to trim jobs or investment.
A small percentage - 10% - said a rate rise would be good for their business.
Meanwhile another survey by business lobby group the CBI found economic growth across the private sector picked up in the three months to December.
The survey of 766 respondents, which comprises economic activity across manufacturing, retail and business and consumer services sectors, found growth improving following weaker figures reported last month.