United have been heavily linked with a move for the England international throughout the summer amid speculation of the former Tottenham defender wanting a Premier League return.
However, no formal bid materialised earlier in the window for Trippier, but as per reports from the Daily Star, Los Rojiblancos rejected their £18m offer on the final day.
Atletico value the 30-year-old at closer to £30m and Diego Simeone was unwilling to lower his asking price at the 11th hour.
Unite’s failure to secure a deal for Trippier also had a knock on effect on their final day plans with Diogo Dalot remaining at the club this season.
The Portuguese star is now likely to be a fringe player at Old Trafford in the coming months as his move to Borussia Dortmund was scuppered by Trippier staying in Madrid.