Greenwood, who has one cap with England, was expected to commit to Jamaica for next week's World Cup qualifiers.
But the former Manchester United star has decided against signing forms to pledge his international allegiences to the Reggae Boyz.
Jamaica coach Steve McClaren admits he's disappointed, but still hopes Greenwood will eventually commit to the island nation.
"We acquired a passport and we expected him to be coming to this camp but in a conversation with his family he's not going to commit at this time to anybody," McClaren said.
"It's a little bit disappointing, we probably have to be more patient. We will keep pursuing him because I know from my conversations with Mason that he loves Jamaica. He wants to concentrate on club football and not commit to an international team at the moment. He's taking his time over that. Who knows in the future?"