Both are set to remain with the club for the coming season under coach Mikel Arteta.
90Min reports the club had conversations about the two and their progress this past season.
Arteta is happy with them and will rely on them this season.
Tierney is the first choice left-back, and Maitland-Niles should see plenty of game time in various positions.
Tierney had been wanted by Leicester City, but that is not a transfer that will be happening now.
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