Saliba has been strongly linked with a move to the Premier League this summer after emerging as one of the most highly-rated defenders in French football having broken into the Saint-Etienne first team last season.
A key man in England's run to the last four of the 2018 World Cup, scoring the opening goal in the semi-final defeat to Croatia, Trippier's form dipped during the course of the 2018/19 campaign.
The England global has been heavily linked with a move away from Spurs this summer, as a number of clubs from overseas circled the 28-year-old.
Biden proposes health law that improves, builds on ACA
Vice President Joe Biden speaks at a campaign stop at Mack's Apples in Londonderry, New Hampshire, U.S., July 13, 2019. He was back in Iowa and touted the public option as "the quickest ... most rational way to get universal coverage".
Spurs signed Trippier from Burnley in 2015 initially to provide back-up for Kyle Walker.
Spurs also had a bid accepted for the defender so says the report, but Saliba has chosen a move to the Gunners over Spurs.
Spurs confirmed that Rose has been granted time off "to explore prospective opportunities with other clubs", along with striker Vincent Janssen and winger Georges-Kevin Nkoudou.
Trippier will be the first English player to play for Atletico in La Liga and the third British player in Spain's top flight next season alongside Scottish forward Jack Harper of Getafe and Real Madrid's Gareth Bale.