The Wanderers sacked Jean-Paul de Marigny on Monday, just three months after appointing him as their full-time coach. On Wednesday, the Jets confirmed they had given their coach Robinson permission to enter talks with Western Sydney.
"Newcastle Jets can confirm that Western Sydney Wanderers have made an official approach for head coach, Carl Robinson," the Jets said in a statement.
"The club has granted permission for the two parties to enter discussions."
Robinson took over the Jets in February, after Ernie Merrick's sacking, joining the A-League club on a three-and-a-half-year deal.
Robinson would become the Wanderers' fourth coach in three years since Tony Popovic resigned after taking the expansion club on a remarkable journey from foundation to Asian Champions League winners in two years.
Popovic also led Wanderers to three A-League championship finals in his five years in charge and although they lost them all, the early success helped make the club one of the best-supported in the Australian top flight.
Harder times have followed since his sudden departure with the club finishing seventh, eighth and ninth in the last three seasons under Josep Gombau, Markus Babbel and, briefly, De Marigny.
The club still has considerable potential, however, especially since they became tenants of the new 30,000-capacity Western Sydney Stadium, which replaced their previous home in Parramatta.
Robinson won 52 caps for Wales in a playing career which included spells at Wolverhampton Wanderers, Sunderland and Norwich City before taking up coaching at the Vancouver Whitecaps in Major League Soccer.
The 2020-21 A-League season is scheduled to kickoff in December.
Information from Reuters and AAP was used in this story.