Mr Shearer stood down as party leader this afternoon, citing discontent amongst his caucus and poor party polling results.
Dr Edwards said David Cunliffe and Grant Robertson were likely to be the two front-runners for the party top spot.
"In that case, I think, Cunliffe probably has the edge, He's the assured performer and he has been a minister before and has a fair degree of public profile and respect already,'' Dr Edwards said.
Mr Cunliffe unsuccessfully challenged the party leadership in November. Following the unsuccessful bid, he was stripped of his portfolios and relegated to the back benches.
Ensuring the party presented a united front for the upcoming election was likely to pull more support for the Cunliffe camp, Dr Edwards said.
"The main thing holding Cunliffe back of course is that he's not particularly well liked by his colleagues.''
However, a number of "wavering voters'' in the Labour caucus would probably shift their support to Mr Cunliffe if he tried for the top position, Dr Edwards predicted.
"I wouldn't be surprised to see something like a Cunliffe - Shane Jones partnership.
"In the last leadership contest, David Cunliffe lined himself up with Nanaia Mahuta and I can't see that happening again.''
A leadership team of Mr Jones, who was present at David Shearer's resignation press conference, and Mr Cunliffe would probably be a "natural fit", Dr Edwards said.
Current deputy leader Grant Robertson would also be a strong contender for leadership.
Andrew Little, who holds the justice and tourism portfolios for Labour, could also be a possible dark horse should he stand, he said.
