She said Birmingham's bid could proceed "subject to that", but also told the House of Commons that bringing the games to Birmingham "would present a unique opportunity for the West Midlands, and it would of course promote global Britain across the Comonwealth."
Birmingham's bid to host the 2022 Commonwealth Games took a huge leap forward last week when it was named as the UK’s candidate city, seeing off a challenge from Liverpool.
The city could now go forward to face potential rival cities from countries such as Australia and Canada in the race to stage the Games and bring thousands of global athletes and visitors to the city.
And city's prospects have received another boost with reports that Kuala Lumpur, the capital of Malaysia, is puling out of the contest.
But the Government will now make a final decision, in consultation with Commonwealth Games England, to decide whether the UK should submit a formal bid to the Commonwealth Games Federation at all.
Staffordshire MP Michael Fabricant (Con Lichfield) urged the Prime Minister to back Birmingham's bid. He told the House of Commons: "Last week in the face of stiff competition, Birmingham defeated the brilliant Liverpool approach and won the award for the Commonwealth Games in the West Midlands, which is excellent news fro the economy not only for Birmingham but also for the greater West Midlands, including Lichfield.
"So would the Prime Minister speak to the Chancellor to ensure that he backs the bid as well, and then bat for Britain to ensure that Birmingham wins the Commonwealth games over Kuala Lumpur?
Mrs May told him: "Obviously the Commonwealth games being hosted in the UK in 2022 in Birmingham would present a unique opportunity for the West Midlands, and it would of course promote global Britain across the Comonwealth.
"The next step is for Birmingham to demonstrate value for money in their bid, but subject to that I've no doubt that Birmingham will continue the UK's rich history of hosting successful sporting events."
Birmingham has not revealed how much it expects hosting the games in the city to cost.
Liverpool previously said hosting the Games would cost £672 million, of which local taxpayers on Merseyside would have to stump up around £137 million.
Birmingham City Council says it as adopted a prudent and innovative approach to minimise costs based on a compact Games.