The plan was suggested yesterday amid growing signs that the left-wing MP will be allowed to enter the race to become the party's candidate for the mayoral election next May.
Labour's selection panel, which meets next Tuesday to draw up the shortlist of party candidates, is thought unlikely to veto Mr Livingstone. There has been intense debate in recent weeks at Downing Street and Labour's Millbank headquarters over whether to exclude him - a move that would enrage many party activists and revive accusations of "control freakery" by Mr Blair.
The so-called "insurance policy" of forcing the eventual candidate to stick to the Government's policies is one reason why opinion is moving towards letting Mr Livingstone stand. Mr Blair wants Frank Dobson, the former secretary of state for Health, to become Mayor but a close contest is in prospect for the nomination.
The "gagging clause" would limit Mr Livingstone's ability to criticise government policies such as the plan for a partial privatisation of the London Underground, which he has repeatedly attacked.
On Tuesday, the panel will ask Mr Livingstone to confirm that he will abide by the rules. Four candidates will be interviewed: Mr Livingstone, the former ministers Mr Dobson and Glenda Jackson, and Ken Baldry, a computer consultant from Islington.Reuse content