According to L’Equipe, the 22-year-old Ghanaian defender only joined the Ligue 1 club last summer but quickly established himself as a key player.
Oppong took advantage of injuries within the Nice defence to become a regular starter, making 40 starts last season.
His impressive performances also earned him a place in Ghana’s squad for the 2026 World Cup, further increasing his profile.
Nice are keen to retain the highly-rated defender but face financial pressure to raise €70 million through player sales and wage reductions before the transfer window closes.
Oppong’s value has risen sharply since his arrival for less than €3 million, with L’Equipe suggesting it may have tripled.
Burnley could face competition from Trabzonspor and an unnamed Ligue 1 club.