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.