Scotland manager defends courting players from south of the Border
Levein is continuing his chase of the Newcastle striker, who has a Scottish grandparent, despite getting little encouragement so far.
The move has not gone down well among some Scotland fans who feel the identity of the national team would be diluted.
But Levein pointed to the make-up of Germany's impressive World Cup team as evidence that Scotland must follow suit. Strikers Lukas Podolski and Miroslav Klose were born in Poland and Germany also fielded Brazil-born striker Cacau.
Levein told Scotland on Sunday: "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."
Levein feels Scottish attempts to unearth eligible players are "amateurish" and he claimed it would have been a "travesty" if Hearts winger Andrew Driver had not been allowed to play for Scotland.
Levein succeeded in making the Oldham-born player a Scotland candidate, despite having played for England at under-21 level, after the SFA pushed for a change to the home nations rule that qualifies non-native players who have attended school in their adopted country for five years.
And he will be similarly determined to persuade Carroll to choose Scotland, with the help of Newcastle first-team coach Colin Calderwood.
"I haven't given up on that one yet, not until he says 100 per cent that he doesn't want to play for Scotland," Levein said. "I have Colin Calderwood there and he is chipping away at him." Among the others who could soon be on Levein's radar are Matt Ritchie of Portsmouth and Jordan Rhodes of Huddersfield Town.
Ritchie qualifies for Scotland through the grandparent rule, and Rhodes was at school in Scotland for more than five years while his father Andy played for Dunfermline, St Johnstone and Airdrie.
Their eligibility was checked out by Levein's chief scout, Mick Oliver, who has been tasked with uncovering Scottish-qualified talent playing in England. Both players are 20-year-old strikers, with Rhodes proving prolific with 23 goals in 52 games for Huddersfield.
It is expected that both will now be considered for Scotland under-21 duty.