The West Ham star is one of 15 UK-based players on Jamaica's radar ahead of next year's World Cup in Qatar.
But, crucially, he didn't make his debut and that has left the door open for the 30-year-old to be approached by the Jamaican FA.
Moyes said: “If he could score a bundle of goals he would come into consideration but when you start with Harry Kane and then you have Dominic Calvert-Lewin and others, then England have a lot of strikers who are scoring goals in the Premier League.
“If I'm looking at it from a distance, Gareth has tended to choose some of the more youthful players over some more senior.
“But if Mick scores a bundle for us and helps us in the run-in then I'm still hopeful it might happen."