Bernstein turns 70 next May and the FA board have agreed to support a move for him to at least stay on for an extra year until after the 2014 World Cup.
That however would require an agreement from the FA shareholders to change the statutes.
A proposal is expected to go forward to allow the chairman to stay beyond the age of 70 but only if they were 69 or under when their final three-year term of office started.
It is understood Bernstein does not have any ambition to go on to stand for a FIFA or UEFA position afterwards.
He will campaign for David Gill, the Manchester United chief executive who is also an FA board member, when he stands for election to UEFA's executive committee next May.
The FA are well aware that Gill's senior position with the most famous club in the world could be a factor for some of the officials from UEFA's 53 member countries who will vote, and Gill and the FA will aim to tackle that issue during the campaign.