New Chivas coach Robin Fraser played with the New Zealand international at the Galaxy in 1999 and 2000 and is believed to be running the rule of him.
Elliott last played in the A-League with Kiwi club Wellington Phoenix in mid November when he was on an injury replacement contract and will now step out for Chivas in a pre-season friendly against his former club San Jose Earthquakes.
Meanwhile, Chivas decided to release 21-year old Colombian defender Yamith Cuesta, who made six MLS appearances last season.
"We decided to part ways with Yamith Cuesta," Fraser said. "He was a wonderful young man. He worked so hard, but I just don't think he was the right fit for what we were looking for."