Macron is searching for his sixth prime minister in under two years and will need to find a personality whose appeal spans the centre-right to centre-left in order to steer a budget through a fragmented and fractured parliament.
The president's office said late on Wednesday that he would name his next prime minister within 48 hours.
Several names have been floating in political circles, including veteran centrist Jean-Louis Borloo, head of the public auditor Pierre Moscovici, and Sebastien Lecornu, who resigned as prime minister on Monday and appeared to rule himself out of contention.
"People tell me 'he's going to test the 'Lecornu 2' hypothesis on you. If that's the case, I wish him good luck," Green party chief Marine Tondelier told TF1 television.
The meeting takes place on Friday afternoon.
France, the euro zone's second largest economy, is mired in its deepest political crisis in decades, turmoil in part precipitated by the president's failed gamble on a snap election in 2024 that weakened further his minority in parliament.
The country's central bank chief, Francois Villeroy de Galhau, forecast the political uncertainty would cost the economy 0.2 percentage points of gross domestic product.
Business sentiment was suffering but the economy was broadly fine, he said.
"Uncertainty is ... the number one enemy of growth," Villeroy told RTL radio.
Fraught budget negotiations in 2025 and 2024 as France seeks to rein in its public finances and tame a gaping budget deficit have cost Macron three prime ministers in less than 12 months.
Villeroy said it would be preferable if the deficit did not exceed 4.8 per centof GDP in 2026.
The deficit is forecast to hit 5.4 per cent in 2025, nearly double the European Union's cap.
Macron's second-to-last prime minister, Francois Bayrou, was ousted by the National Assembly over his plans for 44 billion euros ($A78 billion) in savings to haul the deficit to 4.6 per cent
Rating agencies issued a fresh round of warnings about France's sovereign credit score after Lecornu said his government was resigning just 14 hours after he had announced his cabinet line-up.
