He has strongly denied the accusations and has flagged legal action against certain individuals and organisations for making what he maintains are false claims about his private life.
Gutwein, whose party claimed the seats required to govern in majority on Wednesday night, has stood by Brooks and brushed off suggestions the matter was a gender issue.
“Adam has emphatically denied these matters and I take him at his word,” Gutwein said.
“This is not a gender matter. If Mr Brooks were gay, and two men had made these claims, my position would be exactly the same.”
Gutwein described the allegations as “obviously concerning” and said he would weigh up cabinet positions over the weekend once the final make-up of parliament was decided.