The pair have been dating for about four months and are currently on a romantic vacation in Hawaii.
Aniston, 42, was famously married to actor Brad Pitt, but they divorced in 2005. Pitt went on to have six children with his longtime partner Angelina Jolie.
Theroux, 40, broke up with Heidi Bivens, his girlfriend of 14 years, in March.
"They have talked at length about getting married and starting a family," an insider close to Aniston and Theroux told UsMagazine.com. "She is anxious for the next phase of her life and feels like this is the time."
"They both want it to happen soon," a second source said of the couple's plans to try to have a baby in the near future.
"They are moving quickly, but they know the feelings they have about [each other] are different from past romances," a third friend told UsMagazine.com.
Turkey considering to use pistachios to heat country’s first eco-city
Yosemite climber falls 30 feet, suffers major injuries