Arsenal chairman Peter Hill-Wood insists they will not be panicked into making signings this month and warned that big-money benefactors could be "run over by a bus" and ruin the club.
Arsenal remain in contention for four trophies this season, but there have been calls for further investment during the January window to provide cover for injuries.
Arsene Wenger has said he would be "surprised" if any players joined this month and, while Arsenal has not won a trophy since the 2005 FA Cup, Hill-Wood says the fans should be pleased with the way the club operates.
"It is important for me and the board to not lose our nerve when the media and the fans are all screaming," he said in the Daily Star. "We've had some tough years. Once, in the mid-1980s, I was smuggled out of Highbury, lying in the back of the car.
"We were having a bad run and there were 500 standing outside the boardroom shouting, 'F**k off, Hill-Wood'.
"These days the bar has been raised, but I'm surprised people keep saying Arsenal haven't won anything for five years. Liverpool haven't won the league for 20 years and I remember when they were in the old Second Division and Manchester United were in the old Second Division.
"I think the boys and girls who support us are very lucky."
He added: "I remember a year ago, standing in the front of the directors' box, there was a woman shouting, 'Spend some f*****g money'. I said, 'Don't worry, darling. Leave it to us - we'll sort it out', or some similar patronising statement, which probably p****d her off even more.
"This season we are still in all competitions and second in the league, so we're not that bloody bad!"
Despite suggestions that a rich owner could fund success in the Premier League and Champions League, Hill-Wood, 74, does not feel inviting offers would be to the benefit of the club.
"I don't believe in the way Chelsea and Manchester City have achieved whatever they have achieved," he said.
"It is so much more satisfying to build something - to get boys of 15 to 18 and see them develop sufficiently well to win the Premier League or other trophies - rather than sitting there and saying, 'I want to buy the best striker in the world and I don't care what it costs'.
"A, it is not something we could possibly do and B, even if we could, I wouldn't want to do it.
"If some bloody Russian wants to buy the place and everyone else wants to sell, then, okay, I will go and grow tomatoes in Kent, but if you have a benefactor and he gets run over by a bus, you are gone.
"We have got to have 50,000 people run over by a bus before we have a problem."