The Hammers, who were promoted to the Premier League last season via the playoffs, will discover if their bid for the ground is successful next month.
"Everyone who is a part of West Ham United knows how much it would benefit the club," ESPN quotes Allardyce as saying.
"It would take this club to another level if our bid is accepted. It would be a dream come true and there is nothing I can say more certain than that."
East London outfit Leyton Orient are also in the running to clinch the stadium, situated in Stratford.