Stokes has not been ruled out of the five-test series, but the England and Wales Cricket Board will not consider him for selection until further notice as it awaits developments in the ongoing investigation.
British media then reported that Stokes is travelling to Christchurch, New Zealand to visit his parents Barbara and Gerard Stokes.
The Durham player is still suspended from playing by the European Central Bank pending a police investigation after he was involved in a brawl outside a nightclub in Bristol in September.
"I'll be sat at home watching and following the lads in the hope they do really well", Stokes said in a video.
Stokes was arrested for his part in an incident outside a Bristol nightclub following England's third one-day global victory against West Indies.
He was arrested before being released without charge and police and the European Central Bank are both still investigating the incident. "He is not on his way to the Ashes, England Lions or any other official training camps with the England set-up." the statement read. "His travel arrangements have not been arranged by the European Central Bank".
On Stokes' prospects of playing any part in the Ashes, Strauss added: "We're waiting for the police to make a charging decision and, until that happens, nothing has changed".
The third Ashes Test begins in Perth on December 14, while England start a two-day tour game in the same city on December 9.