May raised the prospect of the World Cup returning to Britain for the first time since 1966 during a visit to Northern Ireland.
Addressing business leaders in the Northern Ireland capital, May said that "both the UK and the Irish governments have already made clear that we would support the tantalising possibility of a joint UK and Ireland World Cup Bid for 2030, should our respective football associations choose to pursue this."
She said family ties and friendship between the two countries are more important than they have ever been. The Irish Prime Minister Leo Varadkar has already said he would welcome a joint bid to host the World Cup.
The football associations of England, Scotland, Wales, Northern Ireland and Ireland are still in talks over whether to proceed with a bid, with a year-long feasibility study needed before any decision is taken.
Qatar is hosting the next World Cup in 2022, followed by a joint tournament in 2026, hosted by the United States, Canada and Mexico.