Former Chelsea boss Claudio Ranieri is also on the short list .
Leicester believe the financial backing they can offer will be enough to tempt O'Neill to quit his job as Republic of Ireland boss and return to club management .
Former Chelsea boss Claudio Ranieri is also on the short list , but Leicester believe the financial backing they can offer will be enough to tempt O'Neill to quit his job as Republic of Ireland boss and return to club management .