The Ivory Coast winger joined the Gunners for a club record fee of £72m in 2019, but he has struggled for form at the Emirates.
Nice are offering a loan deal without an obligation to buy at the end of the season.
The 27-year-old has gone further down the pecking order with the arrival of Gabriel Jesus, Marquinhos and Fabio Viera.
He is yet to play any match for Arsenal this season despite being fully fit.
The Gunners have been linked with a move for Wolves winger Pedro Neto.
Pepe has made 80 appearances for Arsenal, scoring 16 goals in all competitions.
Arsenal have enjoyed an impressive start to the Premier League season, winning their first three matches against Crystal Palace, Leicester City and Bournemouth.
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