Amavi is also interesting Spanish side Atletico Madrid, and Nice's Ligue 1 competitors Lyon, the report states.
The 21-year-old is an intriguing prospect, excelling at left-back this past season for Nice, but also capable of playing in midfield.
He featured 36 times in Ligue 1 this past season, scoring four goals, and is a French under-21 international.
The Spaniard is wanted by La Liga side Athletic Bilbao,reported The Mirror at the end of last month.
Monreal came through a tough start to the season, played out of position in central defence due to an injury crisis, to end the campaign as first choice left-back ahead of England international Kieran Gibbs.
Arsenal have no need to suddenly sell him, but it makes sense to monitor alternatives taking into account the possibility he seeks a move, and Amavi, valued at just £2.2 million by transfermarkt, would be a potentially smart replacement.