INDEPENDENT Kerryn Phelps' stunning by-election result in Wentworth could lead to another outsider putting their hand up for a safe Liberal Party seat in Sydney.

Prominent media commentator Jane Caro is contemplating running against Tony Abbott for the seat of Warringah at the next federal election.

The former prime minister has held the seat since 1994, but Ms Caro could put up her hand for a tilt.

She received strong support on social media following Dr Phelps claiming victory on Saturday night.

"I may not win. Not the point. I feel duty bound to do what I can to stop the climate deniers & the far right destroy my grandchildren's future. If I could help I ought to at least try," Ms Caro tweeted.

She told The Guardianthat she would consider running as an independent.

But first she would have to renounce her British citizenship as she was born in the United Kingdom and moved to Australia as a child.

Tony Windsor, former independent MP for New England, offered his support to Caro on social media.

"The sense of urgency that I feel is felt by a great many people," Ms Caro told The Guardian.

"Particularly climate change is concentrating people's mind.

"Warringah has an awful lot of coast and people there are very much part of enjoying and experiencing and understanding the environment and how it's changing."