With the transfer window set to be closed on August 31, The Gunners are keen to bring the Engalnd international to the Emirates Stadium.
Arsenal right-back Hector Bellerin who could exit the club this summer has still not make any appearance this season.
Despite Arsenal eager to sign Trippier, a report by Eurosport suggests the club is reluctant to settle the current asking price of £34 million for the defender.
Though Atletico are not desperate in offloading one their best defenders who was instrumental in their LaLiga truimph last season but are ready to release him for a right offer.
Trippier has also been link with a move to Manchester United as the Red Devils' first bid was rejected by Atletico Madrid.
But could come back with an improved bid to bring him to the Old Trafford to compete with Aaron Wan-Bissaka for a starting berth at the right-back.
Arsenal's absence from European competitions this season seems to be dragging Trippier back in joining them, having fancied a move to United.
Trippier has featured in all two games for Atletico Madrid in the LaLiga as the side is yet to lose a game.
Diego Simone's side hoping to defend the LaLiga title will host Unai Emery's Villarreal at the Wanda Metropolitano Stadium on Sunday.
Trippier joined Atletico Madrid from Premier League side Tottenham Hotspur in 2019 on a three-year deal, for a fee of £20 million plus add-ons.