Trippier, 28, was excused from Spurs' preseason trip to Singapore to undergo a medical, The Telegraph's Matt Law reports.
It's unclear if Tottenham will sign a replacement for the English international, who's struggled to replicate the highs of a career-best 2017-18 season. Manager Mauricio Pochettino can call upon right-backs Serge Aurier and Kyle Walker-Peters for the upcoming campaign. Juan Foyth, a center-back by trade, can also play on the flank.
Atletico emerged as Trippier's likely destination following the departure of longtime servant Juanfran, whose deal at the Wanda Metropolitano expired at the end of June.