After being the named as the preferred bidder for the ground in Stratford, the 43-year-old says the club will only decide on a proposed move after getting opinions from supporters
Having seemingly fought off interest from Leyton Orient among others, the Hammers could be set to move into the ground in the future, but Brady has stated that they will only push forward if it is the right thing to do for the club and the fans.
"It is important to understand that while the decision represents a huge step forward, as we have stated throughout, preferred bidder status does not mean that West Ham United have at this stage agreed to the move," Brady emphasised in an e-mail to the club's Supporters Advisory Board.
"It remains the case that we will only do so if the final proposal is right for the club and our supporters. This includes the necessity of agreeing a Stadium design specification that is acceptable to us in terms of its ability to host world- class football matches."
Brady has also revealed that she is eager to get the thoughts of West Ham supporters on any potential move, and that she has set up a meeting with 120 fans on the advisory board so that they can get an insight and give their opinion on the move.
"This is the time for supporters to have their voices heard and a more intensive consultation process will commence immediately," Brady continued.
"This must start by working with our Official Supporter Advisory Board to agree how we take that consultation forward.
"We stand by our commitment to conduct full supporter consultation regarding the move, including the polling of supporters."