A survey of 100 MPs, conducted by Dods Polling, found 44% supported the suspension of ministerial responsibility for the EU campaign, while 47% wanted it to stay in place.
Among the 51 Conservatives polled, 20 wanted collective responsibility suspended while 26 wanted it to remain in place.
Of 36 Labour MPs asked the same question, 16 supported the suspension of collective responsibility, while 17 backed it staying in place.
In June, David Cameron accused the media of having “misinterpreted” his comments when he said there could be no “on the one hand, on the other hand approach” to the Government’s stance on Europe.
The remarks had been taken as meaning ministers would be expected to back the Government’s line.