Southampton chairman Nicola Cortese resigned last week following a reported fall-out with Liebherr, sparking fears that manager Mauricio Pochettino could follow.
Pochettino eased those concerns when he insisted he had no intention of quitting, but speculation has mounted that Liebherr, whose father Markus owned the club prior to his death in 2010, is eager to sell.
Liebherr, who took over as non-executive chairman following Cortese's departure, is adamant that is not the case.
In an open letter to fans on the club's official website, she has called for a period of stability following the recent off-field upheaval.
Liebherr said: "The past week has been a period of transition for the club. 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.
"Having inherited Southampton Football Club following my father’s untimely passing, I am delighted and proud of the exhilarating period of success that the team and the staff has enjoyed these past few years, buoyed by the unstinting support of the fans."
The likes of Luke Shaw and Rickie Lambert have been linked with moves away from Southampton this month, but Liebherr has ruled out January depatures.
She added: "I am absolutely committed to ensuring that the club continues this success. I have met our manager Mauricio Pochettino and have given him my complete support to build on the good work that has already been achieved.
"We have also said that we have no plans to sell any of the squad during the January transfer window. Yesterday (Monday) I met the rest of the staff and gave them the same message of support.
"We are now in the top half one of the most competitive leagues in the world, playing attractive football with a young and ambitious team, and poised to move into world-class training facilities.
"We have much to be thankful for. I am particularly excited that the Southampton tradition of nurturing and providing young talent with first team opportunities is set to flourish with the strong academy foundation we have put in place.
"Off the pitch, my priority is to establish the proper running of the club at the top. I also have a strong team of advisers around me as we plan the way forwards. As soon as we have more news to share, we will do so.
"We are looking to the future with a determination to create a culture based on open communication, respect and hard work.
"Finally, let me say this. I will ensure that all decisions made about the future of the club will be in the best interests of its staff, players, management and fans and will be taken with the prime objective of honouring and maintaining the club's heritage and tradition in the Southampton way."
Former Blackburn chairman John Williams is said to be the leading contender to replace Cortese.
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