Parrott started all four of Ireland’s games in the last UEFA Nations League break as Hallgrimsson claimed five points across clashes with Kosovo, Austria and two vs. Israel.
The Dubliner scored four goals in that window, but since returning to his club he's struggled for minutes, despite Cucho Hernandez's injury.
Manuel Pellegrini has only started him in one in the last four LaLiga games, and in his three UEFA Champions League starts in that period, he's not completed 90 minutes once.
His club manager claimed he needs to be rotated after playing multiple games for Ireland, but that was rejected by Hallgrimsson, with the Icelander in no doubt over his talisman.
"Troy pops up and score goals when he wears the green shirt, we know that.
"Hopefully he'll do that tomorrow against Austria. I think it was a good step for him to go to Spain. He's finding his feet and you can see it in his performances there.
"He's growing and understanding better his teammates. But, he's always produced for Ireland.
"Just look at his stats in our last games. I think in the last seven qualifiers, he's scored nine goals, that's pretty good for a national team."
Ireland end their Nations League campaign in Austria on November 14 and at home to Kosovo on November 17.