A feasibility study is under way and will continue before the formal bidding process begins next year.
In an interview with The Sun, the Prime Minister said: "We are very, very keen to bring football home in 2030. I do think it's the right place.
"It's the home of football, it's the right time. It will be an absolutely wonderful thing for the country."
The English Football Association said on Twitter that it welcomed "the Government's pledge of £2.8million towards a potential bid" for the 2030 World Cup.
A joint statement released by the FA and the football associations of Scotland, Wales, Northern Ireland and Republic of Ireland on Monday evening read: "The football associations and Government partners of the UK and Ireland are delighted that the UK Government has committed to support a prospective five-association bid for the 2030 FIFA World Cup.
"We will continue to undertake feasibility work to assess the viability of a bid before FIFA formally open the process in 2022.
"Staging a FIFA World Cup would provide an incredible opportunity to deliver tangible benefits for our nations.
"If a decision is made to bid for the event, we look forward to presenting our hosting proposals to FIFA and the wider global football community."
The 2022 World Cup will take place in Qatar next year, while the 2026 tournament is to be held in the United States, Canada and Mexico.