Ms Archer told ABC radio Hobart, on Monday that she "certainly will consider" throwing her hat in the ring.
"I think I'll just have to wait until the party room meets to see what the final make-up is of the party room, talk to some colleagues and things like that," Ms Archer said.
"I care about where we go to next. I care that we do learn some lessons from this and return to the best interests of Australians and put ideological considerations aside … I will do everything I can to fight to ensure it remains the Liberal Party."
With the Liberal party now in opposition, Ms Archer is determined to carve out her own political identity.
"I think that our politics over recent years, both in Australia and overseas, have become increasingly ideological and tribal. That is not a position that I support," Ms Archer said.
"You have to act in the best interests of the community and the best interests of the country, not in the best interests of partisan politics"
With major key seat swings from Liberal to Labor and moderate independents, the returning member for Bass said the party needed to address the very strong message sent by Australian voters.
"I think there'll be some important lessons to come out of this election. The rise of the independents that we're seeing across the country brings some strong messages for the Liberal party about our future. I look forward to having those discussions after the election [is finalised]," she said.
The Bass Labor candidate Ross Hart has yet to publicly concede the loss.
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