Former Conservative MP Esther McVey has said she would stand in the by-election for David Cameron's seat.
Ms McVey, who represented the party in Wirral West from 2010 until 2015, said it was up to the Conservative Association to choose candidates but suggested she would welcome an invitation to run.
Mr Cameron quit as MP for Witney on Monday, saying he feared becoming a "distraction" for the Government.
Asked if she would stand as Mr Cameron's successor, Ms McVey told Sky News's Murnaghan programme: "I'm flattered that you should think so, but what we believe in the Tory Party is the actual association chooses the candidate, and that's what they'll be doing there.
"So, obviously if the chairman is watching, give us a call."
When asked if she would welcome such an approach, the former employment minister said: "Well, there you go."
Voters in the Oxfordshire constituency of Witney will go to the polls on October 20.
A return to Parliament could see another clash between Ms McVey and Labour's shadow chancellor John McDonnell.
The pair became embroiled in a hostile row in 2014 after Mr McDonnell reportedly made comments about Ms McVey being lynched during a comedy night attended by left-wing activists and fellow Labour politicians.