Macron made the proposal during a lunch, which had not been previously reported, the people said.
The French leader also discussed granting French citizenship to Durov at the time, the newspaper reported.
Russian-born Durov, who holds citizenship in several countries including France, was detained at a Paris airport on Saturday on charges related to the criminal use of his Telegram app, including terrorism, drug trafficking, money laundering and fraud, which could land the 39-year-old billionaire in prison for up to 20 years.
Macron has said that Durov's arrest was not a political decision and promised that the decision on the businessman's case will be made by judges.