Cole, 36, has been linked with a return to England.
"We'll see," said coach Sigi Schmid when asked about Cole's future. "I don't know what Ashley's plans are.
"He still enjoys playing. He'll be the first to say he's not as quick as he was but he has a very good engine, he's very fit, he takes care of himself. As a player, you want to play for as long as you can and for Ashley that could be here."
Galaxy, however, are braced for an extensive team rebuild and Cole takes a valuable international place.
"He still counts as a foreign player," said Schmid to the Daily Mail. "Some guys put in for their Green Card but that's not what Ashley wanted to do. That changes things a little bit. We have to see where we are with our foreign contingent.
"From the point of attitude and the leadership he brings to the locker room and ability to play, so it's definitely something we're going to consider."