The 36-year-old decided against extending his stay in the MLS for another year and will depart Galaxy having scored five goals in 34 appearances for the club.
Donovan, who turns 35 in March, ended a 21-month retirement in September and played well in seven games with the Galaxy, then hinted strongly he wants to play again next season.
The future of LA Galaxy midfielder Steven Gerrard has been the subject of much speculation in recent weeks.
Gerrard has been linked with a return to the United Kingdom, with Celtic reportedly interested in him, while a homecoming to Anfield in some capacity has also been reported.
"I'm going home to spend time with family and decide the best challenge".
Gerrard is out of contract at the end of December.
With Gerrard's days in the Golden State surely numbered, and without any teams lined up to sign him, the player is now faced with the prospect of finally hanging up his boots after 18 years of life as a professional football.
"We were honored to have a player and person of Steven's caliber represent the LA Galaxy over the past two seasons", Galaxy coach and general manager Bruce Arena said in Tuesday's statement. The Galaxy finished ninth and sixth in the MLS table during his two seasons before losing early in the playoffs each time.
Assuming that Rodgers' interest is real and not just more press conference niceties, the obstacles to any such deal materializing have always been finances and the level of interest on the part of the player.
Gerrard, who joined the MLS club after leaving Liverpool in 2015, confirmed he would not return to play for the Galaxy in 2017 following the conclusion of his contract.
He also won two FA Cups, three League Cups and the UEFA Cup at Liverpool, but he never laid his hands on the Premier League trophy.
"Off the coaches and off my team-mates and I'll certainly use that for myself moving forward", Gerrard told reporters.
An open letter to Galaxy fans from Gerrard has been posted on the team Web site.