If both Gabbay and Rousso quit, they would be replaced by the next candidates on the Labor list, former MKs Merav Michaeli and Omer Bar-Lev.
Barak’s return to politics provides the Center and Center-Left with the chance to unseat Netanyahu.
Dance instructor David Landesman joined the Labor race ahead of deadline.
Two years since he was elected to the post of Labor party leader, Gabbay announced on Tuesday that he would not run in the July 2 Labor leadership race.
In a victory for Labor leadership candidate Amir Peretz and Party Secretary General Eran Hermoni, the party will ask members in what manner they wish elections be held.
The proposal to keep the same list of Knesset candidates but with an as yet unselected new leader is expected to be approved in Wednesday's Labor convention.
Meanwhile, Blue and White made a series of decisions on Wednesday about how to run its campaign.
"We will not be a part of the coalition without the finance ministry," the Kulanu party tweeted.
Gabbay led Labor to only six seats in the April 9 election, down from the 24 it won in 2015 as part of the Zionist Union partnership of former MKs Isaac Herzog and Tzipi Livni.
The Likud has been looking for opposition MKs to defect to the coalition in return for portfolios. Channel 12 reported that the Likud had made such an offer to Gabbay.