Gladys Berejiklian, the former NSW Premier who helped lead Australia out of COVID-19 lockdowns, is considering running for federal Parliament, according to people familiar with her thinking.

Treasurer Josh Frydenberg has had several conversations with the 51-year-old to try to persuade her to run in the Sydney seat of Warringah, which is held by independent MP Zali Steggall, one of the sources said.