The Axiom Mission 2 is set to blast off on May 22 at 1.37am GST (May 21, 5.37pm ET), from the Kennedy Space Centre in Florida.
Their stay on the space station was reduced from 10 to eight days to help Nasa adjust its flight schedule.
SpaceX rocket ready to fly
William Gerstenmaier, a vice president at SpaceX, said the rocket was “ready to go fly”.
“We've got the hardware ready to go fly. The Dragon vehicle is over in a hangar awaiting to be attached to the rocket. The rocket is ready to go fly. The pad is ready,” he said.
On Friday, SpaceX will carry out a dry dress, which is a ground test to help measure the readiness of the Falcon 9 rocket.
There is a back-up launch date set for May 23.
But if that opportunity is also missed, the crew may have to wait until the summer, as Nasa and SpaceX will have to prioritise other missions that are coming up.
Mr Gerstenmaier said mission partners Nasa, SpaceX and Axiom Space were tracking the weather for launch day.
“It's still a little bit early to predict the weather. I think we'll know a little bit better in the next couple of days,” he said.
“There's some frontal activity moving through the Florida area. Again, weather's pretty dynamic at this time of year in the spring, but we'll know in the next couple of days and get a better forecast.
“But, right now, our job is to get the vehicles ready, to get the crew through their final training and make sure we're really ready to go fly, and then we'll deal with the weather.”
If the mission goes ahead on May 22, the crew will dock at the ISS later that day at 5.30pm.
The Ax-2 crew members began their mandatory pre-flight quarantine on May 9.
Three Arabs in space together
When the Saudi astronauts arrive on the station, they will join UAE astronaut Sultan Al Neyadi, who is there on a six-month mission.
It will be the first time three Arabs will be in space together at the same time.
Dr Al Neyadi floated his way into history books, as the first Arab astronaut to go on a long-duration space mission and the first one to perform a spacewalk.
He stepped outside of the orbiting laboratory on April 28 for a seven-hour maintenance assignment.
Landmark trip for Saudi Arabia
The Saudi astronauts will become the first citizens from the kingdom to visit the space station.
They are also the first Saudis in space since Prince Sultan bin Salman travelled on the space shuttle nearly 40 years ago.
Saudi Arabia has renewed its space ambitions, announcing a long-term astronaut programme last year.
The Saudi astronauts have been assigned 14 experiments from universities in the kingdom, including ones on cloud seeding.
Mishaal Ashemimry, the microgravity research lead at the Saudi Space Commission, has said the kingdom is considering long-duration space missions next.
“We do have a desire and a goal to have long-stay missions that will capitalise on that microgravity environment,” she said.
“That's essentially what we would like to do with this human space flight programme.
“In doing so, we will train many astronauts, we will engage a lot of local entities to do a lot of research.
“We will also enhance our partnerships with international research entities on collaborative work for microgravity research that spans from human health all the way to physical science.”