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The comments, published ahead of a two-day visit to Corsica, follow protests last weekend that revived long-standing tension between Corsica and Paris less than a month before presidential elections in the euro zone's second biggest economy.
The government is determined to engage in an "unprecedented discussion on institutional matters", Gerald Darmanin told Corse Matin.
"I note that many presidential candidates are in favour of an institutional evolution for Corsica ... We are ready to go as far as autonomy," Darmanin said.
Exactly what autonomous status would mean still needs to be decided, Darmanin said, however. "We need to talk about this, it will take time" the paper quoted him as saying.
Protesters in the northern Corsican town of Bastia attacked public buildings and threw projectiles at police on Sunday after demonstrations in the past week expressed outrage over an attack on a jailed nationalist at a mainland French prison.
Further demonstrations are also expected on Wednesday in the regional capital of Ajaccio, where Darmanin is set to meet local officials.
"We don't have much hope. We don't understand how a minister can come here today and make suggestions, although he does not know if he will still be minister in less than a month," Luc Bernardini of Core in Fronte, a nationalist group, told broadcaster RMC.
"If he's only coming to do us, or himself, a favour, our response will be the same as that of the last days on the streets. The Corsican people will say, 'No'," he added.
In 2003, then Interior Minister Nicolas Sarkozy, who later became French president, was forced to hold a political meeting at a local airport as protesters blocked his arrival on the island.
Darmanin said in his remarks that dealing with the island's status would be a priority during a potential second term in office for President Emmanuel Macron.
Current opinion polls favour Macron as the most likely winner in next month's presidential elections.