The 28-year-old has been capped once by England in a friendly against Wales in 2020 but remains eligible to play for Scotland through his maternal grandparents.
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Scotland boss Clark was hopeful he could persuade Barnes to switch allegiances but has now confirmed the Newcastle man is concentrating on playing for England.
“It’s the perennial question, everybody keeps asking me about it,” said Clarke at the Nations League draw in Brussels.
“This time I can say for sure, Harvey’s going to concentrate on trying to play for England, he’s not going to come to Scotland.
“You can put that one out there. That’s for sure. Nobody needs to ask me or Harvey about it anymore.
“Am I disappointed? No, listen, Harvey can make up his own mind. We move on.”