Greenwood has been outstanding on-loan with Getafe this season after assault charges were dropped last year.
Jamaica have confirmed their hopes to cap Greenwood and Southgate said: I don't think it's something for pre-Euros.
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Allowing him to get his career going again abroad appears to have been a good move. But I have not tracked it closely.
At this moment it would be a big distraction for the team let's see where that leads next season.
I would need to know more details about the whole thing before it was an option."