The race-winning Kiwi was thought to be one of two key contenders for the seat that it set to be vacated by Nick Percat at the end of the current season, along with promising rookie Ryan Wood.
During the recent Sydney SuperNight it appeared Coulthard was the outright favourite for the seat with talk of a single-year deal being on the table.
However the current speculation is that Coulthard has decided not to pursue a full-time return next year, and will instead look to continue with his Carrera Cup programme, and drive for WAU at the Supercars enduros.
That leaves Wood as the obvious choice for WAU alongside star driver Chaz Mostert next year.
WAU team boss Bruce Stewart played a straight bat when asked about his 2024 line-up today ahead of The Bend SuperSprint.
"There's a lot going on," he said of the driver market.
"We're still evaluating. At the moment Chaz is under contract and Nick is under review and we haven't got anything to announce or talk about. We're just working through it."
He did, however, reveal that he wants clarity before the Sandown 500 next month.
"We're working through it and clearly want to have it ratified before we get to Sandown," he added.
The Coulthard news comes amid a number of driver movements for 2024, including a shock return to a full-time Supercars seat for Richie Stanaway.
He is set to join Grove Racing as a replacement for David Reynolds, who is believed to be off to Team 18 with Mark Winterbottom next year.
Triple Eight, meanwhile, has signed Will Brown to replace Shane van Gisbergen, while Jack Le Brocq will replace Brown at Erebus.
