Saliba, 22, was a key part of the Arsenal team that finished runners-up in the Premier League last season. However, his campaign was ended in March by an injury picked up during the Europa League defeat to Sporting CP on penalties.
Arsenal won the first two games after Saliba's injury but subsequently went on a run of just two wins in eight games which led to them being overtaken in the title race by Manchester City.
Saliba has 12 months remaining on his existing deal with Arsenal and sources told ESPN he has committed to the club amid interest from rivals in the Premier League and abroad.
He signed for Arsenal in 2019 from St Etienne but didn't make his first-team debut until this season, spending time on loan to Nice, Marseille and back at St Etienne before breaking into Mikel Arteta's side.