N'Zonzi joined Sevilla from Stoke last summer for a fee of £7m and has impressed in his year-and-a-half spell in Andalousia.
The former Blackburn and Stoke midfielder's form has led to a number of clubs showing interest in him and Guardiola and Conte would like to bring him back to the Premier League, according to the 'Guardian'.
Both clubs will face tough competition, as Barcelona have also been linked with the Frenchman.
N'Zonzi has played 40 times for Sevilla and scored 5 goals. He also won the Europa League last season with the La Liga outfit.