Arsenal chairman Peter Hill-Wood has dismissed Chelsea's plans to become Britain's biggest club as "fantasy".
Hill-Wood spoke out as Arsenal's turnover broke the £200m barrier after their move to the Emirates Stadium.
He said: "I don't want to run Chelsea down, but one has to concede Manchester United and Liverpool are probably the biggest names in UK football.
"For Chelsea to think they are suddenly going to dominate United and Liverpool is fantasy. It is not going to happen."
606: DEBATE
Chelsea chief executive Peter Kenyon has spoken of his desire to "turn the world blue" - but Stamford Bridge has been rocked by the departure of coach Jose Mourinho.
And they attracted a crowd of less than 25,000 for last week's Champions League game against Rosenborg at Stamford Bridge, Mourinho's final game in charge.
Hill-Wood added: "I found it very surprising Chelsea had only 25,000 for a Champions League game.
"We will win the Champions League. It's just when is the question."
"Our fan-base probably started in the 30s and it's been handed down from father to son and so on. It takes 100 years to build and about 100 minutes to destroy.
"Money is irrelevant to history and how big your club is."
Chelsea chief executive Kenyon recently outlined the club's plans to dominate the game under owner Roman Abramovich.
He said: "It's building that dynasty. That's what Roman wants to be part of, Chelsea becoming part of Europe's dynasty.
"Over a 10-year period, you need two European Cups to be a world club. You have to dominate your domestic league. We have to have an infrastructure to deal with that and people to deal with it."
Arsenal insist their financial strength demonstrates they have no need for new overseas investment, and hope to fight off any new moves by Russian billionaire Alisher Usmanov, who is aiming to increase his 21% shareholding.
"If you are contemplating the possibility of dealing in shares, we would suggest that you... consider the stance taken by the directors in committing not to sell their own shareholdings"
Usmanov wants to gain a 25% "blocking stake", which would make the corporate running of the club more difficult without his backing.
Hill-Wood said: "I don't think Roman Abramovich has helped the Russian cause. The board at Arsenal is completely united and has no intention of not remaining so.
"The idea of us selling out to whoever is simply not on the agenda."
And in an open letter sent on Monday, he urged Arsenal's shareholders to think carefully before selling any of their shares.
"The directors of Arsenal continue to hold 45.5% and have no current intention of selling any of their shares," he wrote.
"If you are contemplating the possibility of dealing in shares, we would suggest that you take appropriate financial advice and consider the stance taken by the directors in committing not to sell their own shareholdings.
"We recognise that many shareholders retain shares because they are fans and wish to support the club to the fullest extent possible rather than holding shares solely as a financial investment.
"We welcome shareholders' continued support at this time."
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