Cole, 37, joined LA in 2016 after leaving Roma and was named captain of the team ahead of the 2018 season.
The Galaxy failed to reach the play-offs after a turbulent season and they confirmed on Monday that they would not be retaining Cole for 2019.
Los Angeles Galaxy defender Ashley Cole (3) looks to play a ball during the second half against Toronto FC at BMO Field.
Image credit: Reuters
Cole has given no indication as to his future plans.
Ibrahimovic, who joined the Galaxy for the 2018 season, is still part of the squad as he is contracted until 2019.
However there have been persistent rumours linking him with a move back to former side AC Milan.
Zlatan Ibrahimovic - Los Angeles Galaxy-Red Bulls - MLS 2018 - Getty Images
Image credit: Getty Images
The Swedish forward scored 22 goals in his debut season and was nominated for the league's MVP award alongside Miguel Almiron, Carlos Vela, Josef Martinez and former Manchester United striker Wayne Rooney.
Ibrahimovic was also nominated for the Newcomer of the Year award alongside Rooney and Vela.