The 23-year-old is the Premier League's current top scorer with 23 strikes this season, four more than Harry Kane of Tottenham Hotspur.
Lukaku's future at Goodison Park is uncertain, and the Hammers vice-chair believes that he will only play for a club with Champions League football.
Brady wrote in The Sun: "Romelu Lukaku is a classic shape for a centre-forward - big, broad and decisive.
"We have twice tried to buy him but he wants a club playing Champions League football - and quickly. You can't dismiss his ambition but it's a shame he regards such an admirable club as little more than a stop-over."
Chelsea and Manchester United are among the clubs rumoured to be preparing summer offers for Lukaku.