This new mission, different from the one discussed by owner Elon Musk past year, would have one person fly around the moon in SpaceX's BFR launch vehicle.
It may be noted, in February 2017 SpaceX said that two people have signed a deal with SpaceX to make a trip around the moon aboard - a Falcon Heavy rocket.
Popular Science senior editor Sophie Bushwick on SpaceX CEO Elon Musk's Mars mission project. We're probably looking at years of testing and planning before the BFR is ready to carry a human passenger, and taking them to the moon and back is much different than ferrying someone to the ISS.
The big reveal on who it is - and when the flight to the moon will be - will be announced Monday at the company's headquarters in Hawthorne, California.
He also confirmed that the rendering of the spacecraft in the company's original tweet is a new version of SpaceX's Big Falcon Rocket (BFR). "And they're very serious about it".More news: Chelsea must remain focused after worldwide break - Maurizio Sarri
SpaceX gave no further details, but said more information would follow on Monday.
The new heavy-lift rocket that NASA is developing for deep-space missions - known as the Space Launch System - could serve as a core component of a moon trip.
He has also said that eventually the fleet of SpaceX rockets will be phased out and the BFR will be responsible for all of SpaceX's ambitions.
However the passengers were never named and the flight has yet to materialise.
Stay tuned. We'll have to find wait until next week to learn who will be aboard the round-the-moon flight.