As part of a programme called Artemis, Nasa will send a man and a woman to the lunar surface in the first landing with humans since 1972.
But the agency's timeline is contingent on Congress releasing $3.2bn for building a landing system.
Astronauts will travel in an Apollo-like capsule called Orion that will launch on a powerful rocket called SLS.
NASA administrator Jim Bridenstine said: "The $28bn represents the costs associated for the next four years in the Artemis programme to land on the Moon. SLS funding, Orion funding, the human landing system and of course the spacesuits - all of those things that are part of the Artemis programme are included."
But he explained: "The budget request that we have before the House and the Senate right now includes $3.2bn for 2021 for the human landing system. It is critically important that we get that $3.2bn."
The US House of Representatives has already passed a Bill allocating $600m towards the lunar lander. But Nasa will need more funds to develop the vehicle in full.
Mr Bridenstine added: "I want to be clear, we are exceptionally grateful to the House of Representatives that, in a bipartisan way, they have determined that funding a human landing system is important - that's what that $600m represents. It is also true that we are asking for the full $3.2bn."
In July 2019, Bridenstine told that the first woman astronaut to walk on the Moon in 2024 would be someone "who has been proven, somebody who has flown, somebody who has been on the International Space Station already". He also said it would be someone already in the astronaut corps.
At the time of this interview, there were 12 active woman astronauts. They have since been joined by five other female Nasa astronauts who graduated from training earlier this year. But it remains unclear whether any of the newest astronauts can fulfil the criteria in time to fly on the first landing mission in 2024.
Asked about the timeline for choosing crew members for Artemis, the NASA chief said he hoped to pick a team at least two years prior to the first mission.
However, he said: "I think it's important we start identifying the Artemis team earlier than not... primarily because I think it will serve as a source of inspiration."