The 29-year-old midfielder is currently away on international duty with England, hoping to force his way into Fabio Capello's 23-man World Cup squad.
He has been thrust into contention for a place on the plane to South Africa after an impressive season at domestic level.
Parker helped to spearhead the Hammers' survival bid last term, leading by example on and off the field.
Having set impeccably high standards, he has inevitably been dragged into the transfer rumour mill - which is now at full throttle.
Various Premier League clubs are reported to be weighing up an approach, with Aston Villa among those said to be keen.
West Ham have no plans to part with their skipper, though, and Brady insists there is no chance of the board sanctioning a sale.
"It's interesting that David Sullivan has given his word that Scott Parker will not be sold and I think that's absolutely what we wish to deliver to the supporters, that he's not going to be sold," Brady said.
"So I think Aston Villa should reconsider making any approach because the worst thing is that it's very unsettling for the player, very unsettling for the club.
"I think if we wanted to sell him we'd go about it a different way but we really don't. He's the player of the year and he's very important to us in building a better team to take West Ham into a better future."