Mr Wilmore, 61, and Ms Williams, 58, flew a Boeing Starliner spacecraft to the station. It was the first flight of its kind with people on board and was a test designed to see how the new spacecraft performs before it is used more regularly.
Problems, however, emerged as it made its approach. These included leaks in its propulsion system and some of its thrusters shutting down.
So while they made it to the space station safely, they will need an alternative mode of transport to get home if the Starliner is not deemed safe to return to earth.
At a news briefing on Wednesday, Nasa officials said no firm decisions had been made when it comes to next steps.
"Our prime option is to return Butch and Suni on Starliner," Steve Stich, manager of NASA's Commercial Crew Program, said. "However, we have done the requisite planning to make sure we have other options open.”
One potential option being considered, they said, is to attach the two astronauts to a mission that is scheduled to launch in September, and return them to earth with that mission in February 2025.
That flight to the space station will be made by a SpaceX Crew Dragon craft. The initial plan was for four crew members to be aboard, but two of the seats could be left empty if needed.
That plan would mean the astronauts would spend more than eight months – rather than eight days – aboard the International Space Station.
If the Crew Dragon is used, the Starliner craft would be returned to earth without any crew, under computer control.
Nasa officials said it could take a week or more for a final decision to be made.
Ken Bowersox, NASA's director of space operations, told reporters the chances of an uncrewed return of the Starliner “have increased a little bit based on where things have gone over the last week or two.”
"That's why we're looking more closely at that option to make sure that we can handle it," he said.
Using a SpaceX craft to return the astronauts would be a blow to Boeing, which has for years tried to compete with the company and its more experienced Crew Dragon.
Earlier this week, Nasa used a SpaceX rocket to deliver more food and supplies to the ISS, including extra clothes for the two astronauts.
Last month, in a short press briefing, the pair said they were "absolutely confident” in the return trip and Starliner was “truly impressive.”
