The proposal for an alternative press regulator put forward by three major newspaper groups would, controversially, give newspapers the ability to veto appointments to the board, the Guardian reports.
This is likely to be a sticking point since the Labour party and campaign group Hacked Off believe that newspapers must not have so much influence over who runs the future regulator.
The Guardian reports the right of veto given to newspapers bosses was seen as one of the major weaknesses of the discredited Press Complaints Commission.
Proponents of the alternative regulator say appointments to the board would be "without any direction from industry or influence from Government".
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