But none of the leadership candidates, Keir Starmer, Rebecca Long-Bailey, Lisa Nandy and Emily Thornberry, are advocating the party adopt a rejoin platform.
The former PM - who was forced to quit after a wave of resignations sparked by the Chris Pincher scandal - is taking soundings from his supporters before making a final decision.
When he resigned, he described being PM as “the best job in the world”.
He is currently in the Caribbean on holiday, but is preparing to cut it short to fly back to London before making a final decision.