The club were recently named as the No.1 choice to move into the £429m venue and they will now give their fans the chance to air their views.
The London Legacy Development Corporation (LLDC) made the announcement last week, although there are a number of loose ends to sort out before the deal is finally completed.
The SAB will discuss the LLDC's decision at Tuesday's emergency meeting which will be attended by vice-chairman Karren Brady, joint-chairman David Gold and ex-West Ham striker Tony Cottee.
A statement on the club's official website reads: "The LLDC decision represents a huge step forward but, as the club has stated throughout, highest-ranked bidder status does not mean that West Ham have at this stage agreed to the move and it remains the case that we will only do so if the final proposal is right for the club and its supporters.
"The time for supporters to have their voices heard is now and a more intensive consultation process will commence on Tuesday evening.
"The club will consult with SAB members to agree how the club takes that consultation process forward.
"The club stands by its commitment to conduct full supporter consultation regarding the proposed move, including the polling of supporters.
"West Ham fans can be confident that wherever there is an opportunity for West Ham to input in the decisions going forward, supporters will be at the forefront."
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