The PM will host a meeting of officials from football governing bodies the FA and the Premier League, as well as fans’ representatives, later to discuss the proposed European Super League.
Boris Johnson described the new league, which includes six leading English clubs, as “ludicrous”.
The 12 founding members of the league face a fierce backlash after unveiling proposals for a breakaway tournament.
One insisted they were doing it to “save football”.
Real Madrid President Florentino Perez said the decision to create the new league, which his club would be a part of, was in part taken because “young people are no longer interested” in the game.
He told a Spanish TV show: “Audiences are decreasing and rights are decreasing and something had to be done. We are all ruined. Television has to change so we can adapt.”
The 14 Premier League clubs not participating in the new venture are also due to discuss their response later.
Fans and pundits have expressed fury at what they say would be an unfair competition that would lock many teams out of top European football.
The proposed league – which has been described as a football “closed shop” by a government minister – has united MPs from every party against it.
Under the plans – revealed on Sunday – the 12 founding football clubs would be permanent members and never face relegation.
Critics say the new league could supplant the existing Champions League and disrupt the current football “pyramid” that sees teams rise or fall on merit.
‘You can see the anger’
Writing in the Sun, the prime minister said he was “horrified” at the implications for clubs across the country.
In a direct message to fans, he said: “It is your game – and you can rest assured that I’m going to do everything I can to give this ludicrous plan a straight red.”
Former England captain Alan Shearer told BBC Breakfast the six English clubs should be expelled from the Premier League, which they have said they aim to remain in while also playing in the European Super League.
“It’s not right what they are doing, it’s not competitive, it’s a closed shop – you can’t have a competition where no one else is allowed in,” he said.
“You can hear, feel and see the anger from almost everyone in football.”
Labour’s shadow sports minister Alison McGovern urged the UK’s competitions watchdog to investigate, describing the plans as “nothing short of an attempt to stitch up competition for a few elite clubs at the top”.
And on Monday, the Duke of Cambridge, who is president of the Football Association, said he shared fans’ concerns about “the damage it risks causing to the game we love”.
Meanwhile, the president of European football’s governing body Uefa, Aleksander Ceferin, warned players who play for teams in the ESL that they would be “banned from the World Cup and the Euros”.
Sky Sports confirmed it had not “not been involved in any discussions” about the breakaway league.
“We are completely focused on supporting our long term football partners in the UK and in Europe,” the broadcaster said.
How would the European Super League work?
Six English clubs – Arsenal, Chelsea, Liverpool, Manchester City, Manchester United and Tottenham – have signed up to the league.
They would join Spanish sides Atletico Madrid, Real Madrid and Barcelona and Italian clubs AC Milan, Juventus and Inter Milan.
The competition would have 20 teams and another five sides would have to qualify each year for the competition.
Matches would take place midweek and rival the existing Champions League.
Read more here.
On Monday, Culture Secretary Oliver Dowden said if football authorities could not prevent English clubs from joining the ESL, the government would do “whatever it takes” to protect the national game.
He added club owners “should remember that they are only temporary custodians of these clubs and that they forget fans at their peril”.
Kevin Miles, chief executive of the Football Supporters’ Association, said the new league “smashes that dream” for a fan of their team being promoted.
“It’s based on power, it’s based on greed, it’s based on money. It’s not based on sporting achievement,” he said.
Speaking to BBC Newscast, Mr Miles said the government “could make life very difficult” for participating clubs: “There’s tax exemptions, all sorts of things that these elite clubs enjoy, that government could interfere with.”
There were protests outside grounds around the country on Monday, with fans of both Liverpool and Leeds gathered outside the Yorkshire club’s Elland Road stadium before their evening fixture.
Leeds players wore T-shirts saying “Earn it” next to the Champions League logo and “Football is for the fans” and left the shirts in Liverpool’s dressing room in case they wanted to join the protest.
A plane also flew overhead with a banner saying: “Say No To Super League.”