Fraser Kemp, the party's former general election co-ordinator, said even cabinet ministers should be subject to Millbank approval.
Mr Kemp, MP for Houghton and Washington East, said the system would root out members who attacked the Government "every five minutes".
The suggestion, backed by senior officials, is likely to be seen as a "softening-up exercise" ahead of a move to introduce the change at the next party conference. MPs would be interviewed by an NEC panel similar to those set up to vet candidates for councils, the Scottish Parliament, Welsh Assembly and London mayoralty.
Critics say the system has been used to block left-wing candidates in Scotland and Wales and will be used to halt Ken Livingstone in London.
Current rules allow MPs to stand again if they get the backing of their local party, but all other Labour candidates face rigorous training and interviews.
Mr Kemp said it was time to end such a system. Vetting panels were "not centralised control, but common sense", he told The Independent. "If we are to be consistent, it has to apply to Westminster MPs ... I look at this from my own history as a party official ... I saw the impact of a few self-indulgent people. They enabled our opponents to paint us as extremist, divided and out-of-touch."
A party spokesman said there were no plans to change the system, because to do so would make "martyrs" out of a handful of difficult MPs.
A backbencher said the plan was sure to cause uproar if Blair supporters tried to push it through the conference. "This would be the worst example of control freakery yet. Has Millbank finally gone mad?"Reuse content