The 30-year-old is believed to be linked with a move to Manchester United in the current market.
A recent report suggested that the Red Devils are still working on a deal for the England international, who is valued at €40m by the Spanish champions.
However, according to The Sun, there is also firm interest from Arsenal, with the North Londoners keen to sign a replacement for Hector Bellerin.
The report adds that the Gunners are yet to make an official offer for Trippier, whose contract is due to expire in June 2023.
The Englishman previously spent four years at Tottenham Hotspur before moving to La Liga.