One of Tony Abbott's key political allies in Warringah has warned Zali Steggall would face a preselection battle against "very well-qualified" candidates should she make any shock mid-term switch to the Morrison government.

The independent's first days in Parliament have been overshadowed by a reluctance to categorically rule out joining the Liberal Party, despite defeating its former leader in a contest for the blue-ribbon Sydney seat at the May 18 election.

Independent MP Zali Steggall in Parliament on Thursday. Credit:Alex Ellinghausen

Roger Corbett, a former Woolworths chief executive and one-time chairman of Fairfax Media who is now president of the party's federal electorate council in Warringah, told The Sydney Morning Herald and The Age he was "surprised" by speculation about Ms Steggall's future.

"Warringah is a very important seat and of course has had a Liberal tradition," Mr Corbett said. "And it would be my expectations that a large number of very well-qualified people might seek preselection for this seat.