Cortese resigned as chief executive last Wednesday, meaning Liebherr became non-executive chairman, with speculation rife that manager Mauricio Pochettino - a close friend of Cortese - and several key players could follow the Italian out of St Mary's.
Pochettino has since said he intends to remain in charge and Gareth Rogers has now been appointed as interim chief executive officer, with Liebherr telling the fans she wants to continue to take the club forward.
"The past week has been a period of transition for the club," she said in a statement issued on the club's official website.
"I wanted to address you directly to clearly set out my position and expectations for the immediate future. After the developments of last week, my priority now is to bring some stability and calm to the workings of the club; perhaps a few smiles too."