The Prime Minister signalled she would offer Government support if the Football Association decides to move forward with an official bid.
The FAs of England, Scotland, Wales, Northern Ireland and Ireland are currently undertaking feasibility work and considering putting forward a proposal.
Mrs May, speaking on eve of the Conservative Party conference in Birmingham, said: “Following the excitement of this Summer’s World Cup, the English FA are working together with the FAs of Scotland, Wales, Northern Ireland and Ireland to explore whether there could be a joint bid to host the 2030 World Cup.
“The decision on whether to bid is, of course, for the football associations to make. But if they decide to go forward, they can count on this government’s full support.”
The news comes as Education Secretary Damian Hinds and Sports Minister Tracey Crouch announce they will lead a new cross-government action plan to improve competitive school sports.
They will convene key organisations in the sports world - including the Premier League, the FA and the RFU - to agree a new plan on how to get more kids playing competitive sport.
London and Glasgow will host eleven games in the UEFA European Championships in 2020 with Wembley hosting the semi-finals and the final.
In the last six years the UK has successfully hosted the London 2012 Olympic and Paralympic Games, the 2013 Rugby League World Cup, the 2014 Commonwealth Games in Glasgow, the 2014 Tour De France Grand Depart and the 2015 Rugby World Cup.
Any England bid would face opposition from the joint campaign of Uruguay, Argentina and Paraguay which could be buoyed by the fact 2030 marks 100 years since the first World Cup, held in Uruguay in 1930.
It is also possible there will be an African bid, especially in light of Morocco’s defeat to the USA for the 2026 tournament.