This week former prime minister Manuel Valls shocked his Socialist party by saying it was "dead" and announcing he wanted to be a candidate under Macron's banner.
In late March, Valls declared his support for Macron rather than for the candidate of his own Socialist Party (PS), Benoit Hamon, who ended up eliminated in the first round of the presidential election.
Mr. Macron won the presidency with 66% of votes against his far-right rival Marine Le Pen's 34%, show the final numbers released by France's Interior Ministry.
A representative of Republic On the Move said Wednesday that Valls had "not yet" fulfilled the criteria to be a candidate.
"All support for the president is welcome", said Jean-Paul Delevoye, head of the En Marche selection panel.
Before the French election, a wide coalition of interests, stretching from Beijing to Washington, feared the consequences of a Marine Le Pen victory.
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The news sends a signal to politicians to the left and right of Macron's year-old Republic on the Move party that they can not sit on the fence as they seek to position themselves for the June elections that will complete the political landscape for the next five years.
At Macron's victory party outside the Louvre on Sunday, the classical music lover walked on to the stage to the strains of "Ode to Joy", the anthem of the European Union, rather than France's La Marseillaise, which was saved for the end of his speech. The poor result has triggered a fierce debate within the Socialists about whether to stick with Hamon's left-wing platform or to switch back to the more centrist views of Valls and his allies.
On Monday, the chief of Macron's movement, Richard Ferrand, said it would modify its name to "Republic on the Move" so as to structure itself more like a traditional party.
The party was due later on Wednesday to work further on what Baroin said would be a revamped program for the National Assembly election.
French President-elect Emmanuel Macron.
The right-wing Republicans party is seeking to win enough seats in parliament to force Macron into a power-sharing deal.
Macron, who will be inaugurated on Sunday, has said he is aiming for an absolute majority in the lower chamber in June's elections.