Turnbull government MP John Alexander is scrambling to confirm whether he is a dual citizen, which if proven would trigger a byelection that would further threaten the Coalition's grip on power.

Fairfax Media can reveal Mr Alexander's father, Gilbert Alexander, was born in the UK and is likely to have conferred citizenship by descent to his son. Mr Alexander has never before been named as an MP with a parent born overseas, meaning his status has flown under the radar since the citizenship saga first erupted in July.

The Liberal member for the Sydney seat of Bennelong has confirmed he never renounced any British citizenship before entering Parliament, and cannot say definitively whether his father did so before the former tennis champion's birth in 1951.

This means he could be ineligible for Parliament under section 44 of the constitution.