Investigators may try to obtain additional information from Durov for the investigation or put pressure on him by extending his detention, the report said on Tuesday.
If Durov is charged "it will be interesting to see what measures a judge imposes, as he lives abroad," the lawyer was quoted as saying by the newspaper, adding that house arrest or a ban on leaving the country could be imposed.
Durov may be in custody at the National Anti-Fraud Unit in the suburbs of Paris, a source told RIA Novosti.
"Considering that the investigation of his case has been entrusted to the National Anti-Fraud Unit, Durov may be there," the source said.
Russian-born Durov, who is a citizen of multiple countries, including France, was detained at an airport north of Paris on Saturday on charges linked to criminal uses of his Telegram app, including terrorism, drug trafficking, money laundering and fraud.