Top-flight football has been criticised for its lack of entertainment value recently, with Chelsea already six points clear at the top without conceding a goal in the league.
Whelan believes a salary cap would create more competition for Chelsea - who are backed by billionaire Roman Abramovich - which would in turn create more excitement for fans.
"I would like 20 players registered with a salary cap, a figure that each team agrees on," Whelan said.
"You might get Manchester United or Arsenal supporting it on the basis they can see Chelsea ruining this league. Last season there was more interest in the bottom than there was at the top of the league."
Whelan added: "This is not something I've just brought up, it's something I've been advocating for five or six years. If this continues then the league is over in the next four or five weeks. Manchester United have debts and Arsenal are funding a new stadium - it's Chelsea on their own.
"Good luck to Chelsea, I've got nothing against them but the competition has gone. If Mr Abramovich chooses to stay there and they continue with building their squad, nobody in the league can compete with that."
Attendance figures for top-flight matches have dropped recently, and Whelan believes it is because staying in the league has become increasingly important.
"Why is it boring? Because we are all fighting for survival," Whelan added. "You get the likes of Bolton, Blackburn and Sunderland - even Everton - having to fight like hell just for survival in the league."
Critics of a salary cap would suggest the better players would then move to a foreign league where they would be paid more, but Whelan countered: "There will be more British players in the league, which is a good thing. They (foreign teams) will follow when they see how beneficial it is."
The salary cap has been a success for rugby league, although Wigan Warriors - where Whelan is a director - were unhappy with a reduction in the cap last year.
"We were all a bit sceptical but it has worked," Whelan added. "Wigan are not even in the play-offs this year, a few years ago it was not a case of 'will Wigan win' it was a case of 'how many by?"'
Sunderland boss Mick McCarthy agrees with Whelan that teams are now trying to avoid defeat at all costs, but he does not believe a salary cap will be introduced.
"It is not going to happen," McCarthy said. "We are in a free world, really, and someone like Chelsea can do what they have done. How can they stop that happening? I do not know."
The Black Cats boss added: "They go out, some teams, and do not want to be beaten first and foremost, which should always be the way you look at it - you do not want to concede goals, you do not want to be beaten."
Meanwhile, Liverpool manager Rafael Benitez believes there is much more excitement to come in the Premiership this season.
"It is still the start of the season and teams will get better as time goes by," he insisted. "Teams don't want to concede goals at the moment but games will soon become more open again."
Norwich were relegated last season but their chief executive Neil Doncaster believes there are a number of reasons why the top flight is suffering from a fall in attendances.
He said: "High prices are really only part of the story. The reasons why supporters are turning away from the Premiership are many and varied.
"The sort of football supporters want to see demands the domestic league is a competitive one. With Chelsea six points clear, it is hard not to be turned off by Premier League football.
"The constant changing of fixtures to suit television and the bizarre scheduling of matches are equally to blame. The number of Premiership matches taking place on Sundays, when rail engineering works frequently lead to already reduced services being interrupted or replaced by buses, are hardly an incentive to travel hundreds of miles to support your team.
"To add to the problem, Sky subscribers can now view extended highlights of their team the very same evening without having to leave their living room."