Levein is continuing his chase of the Newcastle striker, who has a Scottish grandparent, despite being told by Carroll to forget it.
The move has not gone down well among some Scotland fans who feel he has embarrassed himself enough.
Craig Levein: "I hear people say 'oh this player or that player shouldn't play because he is not Scottish'. But Germany did well at the World Cup and they have guys from all over the place.
"The rules are there and other people are using the rules.
"And while there might have been some people sitting there with their arms crossed, determined not to celebrate when they beat England or Argentina because a certain guy is Polish or whatever, the majority supported the team.
"We just want to win and if we do that it covers up a lot of these problems and the majority of Scottish fans will be happy.
"I haven't given up on Andy Carroll yet, not until he says 100% that he doesn't want to play for Scotland," Levein said.
"I have Colin Calderwood down there and he is chipping away at him."