The former vice-chairman is eager to return to the Gunners board, after being ousted last season after being heavily involved in bringing onboard American Stan Kroenke, to the dismay of several other major shareholders.
Dein sold his stake in Arsenal this week to Uzbek billionaire Alisher Usmanov for £75million, before being immediately installed as chairman of Red and White Holdings.
"We can all live in a comfortable, closeted world where we're happy for a football club to be making £20million or £30million a year," Dein told the News of the World.
"I'm not talking about this year, or even next year - but in three years' time I firmly believe Arsenal will be blown out of the water unless the board open the door to new investment.
"If Arsenal are to have a realistic chance of winning the Premier League in the future, then the club has to accept they will need a huge injection of money.
"Everybody has seen what Chelsea have done and they are there for the long term.
"Arsenal say they are in great shape today but we're not talking about today.
"We are talking about the future. Unless the current board realise you cannot judge things by this year's standards or even next year's, then I'm afraid we're going to get left behind by others - and that would break my heart."