Keane - voted the league's most valuable player last week - scored a 111th-minute winner as the Galaxy defeated New England Revolution 2-1 in the MLS Cup on Sunday.
But the 34-year-old Republic of Ireland international's exploits in the season-decider may have been his last in a Galaxy shirt.
Keane - who has another year remaining on his contract - said he needs time to think about his future.
"I definitely need to recharge the batteries and see what the next chapter is for me, whether it's here or it's somewhere else...," said Keane, who swapped Tottenham for Los Angeles in 2011.
"I'm not saying I'm going to leave but what I'm saying is I need to consider what I want to do, you know?
"Sometimes change is good for everybody."
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