The newly-elected 39-year-old president had promised in March on the campaign trail to create "a real status" for his wife Brigitte, who is his former schoolteacher.
The issue has become a new political headache for Macron after an online petition against creating the role garnered around 270,000 signatures and an opinion poll showed a majority of French people were also opposed.
The presidency will clarify Brigitte Macron's position in the coming days, a source told AFP late on Monday, adding that there were would be no change to the constitution to create a First Lady position.
Instead, the presidency will make clear the resources at Brigitte Macron's disposal and the cost to the public purse.
"The idea is for the French people to know how much this role costs," Aurore Berge, a senior lawmaker from Macron's Republic on the Move party, told Europe 1 radio on Tuesday.
The new status would have seen France copy the American tradition of a prominent public role for the First Lady. Neither country has ever had a female head of state.