Cambridgeshire councillor Lisa Duffy, the runner-up in UKIP's leadership election, says she is thinking of standing again.
Ms Duffy said she was disappointed but not surprised by the resignation of UKIP's new leader Diane James and accused her of not showing sufficient leadership.
Ms Duffy said she would now talk to her family and supporters about running in the new leadership election.
She finished second in last month's leadership election, gaining 4,591 votes. If she did run again, she is likely to face tough opposition from North-West England MEP Steven Woolfe who was controversially blocked from standing last time.