Instead, she reportedly wants the case to be handled by a private judge, who can help the process to move much faster than the courts.
Affleck and Garner originally announced their separation in 2015, filing for divorce two years later, and sources say Garner wants to have a divorce decree by the end of the year.
"After much thought and careful consideration, we have made the difficult decision to divorce," they said in a statement at the time. "We go forward with love and friendship for one another and a commitment to coparenting our children whose privacy we ask to be respected during this difficult time. This will be our only comment on this private, family matter. Thank you for understanding."
Affleck's drinking was reportedly a major reason for the divorce stalling, with sources saying that Garner did not want to set a custody agreement until the actor was sober. The couple shares three children, daughters Violet, 12, and Seraphina, 9, and son Samuel, 6.
"Jen wanted to give Ben the time and opportunity to work on his health and sobriety," a source previously told Us Weekly. "She isn't in a rush...Jen just isn't willing to settle the custody issues until she's 100 percent certain that he's clean."
It was reported in August that Affleck had entered treatment at The Canyon at Peace Park in Malibu after an intervention by Garner.
"He is seeking treatment," a source told PEOPLE of the actor. "He knew he needed help and was vocal about it."
In March 2017, Affleck revealed in a Facebook post that he had completed treatment for alcohol addiction.
"I have completed treatment for alcohol addiction; something I've dealt with in the past and will continue to confront," he wrote. "I want to live life to the fullest and be the best father I can be. I want my kids to know there is no shame in getting help when you need it, and to be a source of strength for anyone out there who needs help but is afraid to take the first step," he continued. "I'm lucky to have the love of my family and friends, including my co-parent, Jen, who has supported me and cared for our kids as I've done the work I set out to do. This was the first of many steps being taken towards a positive recovery."
Photo Credit: Getty / Axelle/Bauer-Griffin