Valls resigned his post last week to fight for the nomination after deeply unpopular Socialist President Francois Hollande announced he would not seek a second term in office.
Hollande's decision means his Spanish-born former premier is the favourite to win the two-round Socialist primary on January 22nd and 29th.
But whoever comes out top will plunge into a presidential race already dominated by rightwing candidate Francois Fillon and far-right leader Marine Le Pen.
Polls show they will be the two candidates who make it through to the second round of the presidential election in May.
The two other leading candidates on the French left -- which is bitterly divided after four years in power -- are reform-minded former economy minister Emmanuel Macron and the hard-left Jean-Luc Melenchon, who are bypassing the primary to run as independent candidates.
Valls meanwhile must fight his campaign with the government's questionable record on reducing unemployment hanging round his neck.
The final list of candidates will be unveiled on Saturday, the Socialist party said.
The contenders then face three televised debates in the space of just eight days between January 12th and 19th before the first round of voting.
The two finalists will then face off in a final debate on January 25th before the decisive vote four days later.
'I am not favourite'
Four other former ministers under Hollande are also seeking the Socialist nomination -- ex-economy minister Arnaud Montebourg and two men who held the education portfolio, Benoit Hamon and Vincent Peillon.
As in last month's rightwing primary, just one woman is among the candidates, 39-year-old former housing minister Sylvia Pinel.
The hopes of environmentalists rest with Francois de Rugy while a member of the European Parliament, Jean-Luc Bennahmias, is another outsider.
A poll last week showed Valls was the preferred Socialist candidate with 24 percent compared to 14 percent for Montebourg, when voters of all political colours were taken into consideration.
When only leftwing voters were asked, the survey by Harris Interactive found Valls was again the most popular with 33 percent to 20 percent for Montebourg.
Valls, perhaps mindful of the dramatic turnaround in the rightwing primary that saw Fillon emerge victorious, has dismissed talk that he is the leftwing frontrunner.
"I am the challenger in this presidential election. I am not going into it with the idea that I am the favourite for the primary," the 54-year-old said on Tuesday.
In the race for the right, former prime minister Alain Juppé began the contest as the clear favourite but was easily beaten in the runoff by Fillon, another former premier who had begun the race languishing in third place.
Macron, already on the campaign trail, has been scathing about his former cabinet colleagues.
"For 18 months now, (polls show) the left will be eliminated in the first round" of the presidential election, he said.
Macron claims he is trying to reach out to "neither right nor left".
Given the fractured state of the left, Socialist officials admit turnout is unlikely to rival the 2.7 million who took part in the 2011 leftwing primary.