On Monday, Macron held two meetings with potential candidates: one with the Republican former minister Xavier Bertrand and one with the Social Democratic former Prime Minister Bernard Cazeneuve.
The President "is testing both hypotheses", sources with insight into the talks told AFP and other French media.
In the French parliamentary election last summer, the left-wing alliance New People's Front received the most seats. However, neither the left, Macron's center alliance, nor the growing far-right party National Rally received enough seats to be able to govern on their own.
Prime Minister Gabriel Attal has remained in office during difficult government negotiations, where Macron has faced accusations from both the right and the left of not being willing to meet them halfway.
The left-wing candidate Lucie Castets has already been rejected by the President, who did not believe she had any chance of gathering a majority behind her.
The leader of the Republicans has informed the President that they would support a choice of Xavier Bertrand, which would mean that there would at least almost be a parliamentary basis for it.
However, the Nationalists' leader Jordan Bardella is warning that they will move forward with a vote of no confidence against Bertrand if he is appointed, as they want to see a technocratic government tasked with fundamentally reforming the electoral system.