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Gyokeres signed for Arsenal from Sporting CP last summer for a fee in the region of £54m and scored 21 goals in 55 games across all competitions last season.
His arrival ended Arsenal's pursuit of a centre-forward, with Gyokeres targeted after 97 goals in 102 games across two seasons with Sporting.
The Swedish striker was Arsenal's leading scorer as the Gunners ended a 22-year wait for the Premier League title, but was a target for criticism throughout much of the campaign.
Arsenal are ready to consider suitable offers for the 28-year-old in this summer's transfer window, with Kai Havertz preferred at centre-forward for the Champions League final defeat to Paris Saint-Germain.
Arsenal are working on a deal to sign Bruno Guimaraes from Newcastle United, and are also pursuing Vinicius Junior, as contract talks stall at Real Madrid.
The investment required to secure the double signing means sales are expected, with The Independent reporting that Gyokeres is a player Arsenal will consider selling for the right fee.
Atletico Madrid had been named as a potential destination, should Julian Alvarez depart. Barcelona are pursuing a deal to sign Alvarez, while Atleti have also seen Antoine Griezmann leave for MLS side Orlando.
Also available for sale this summer at Arsenal are Reiss Nelson, Gabriel Jesus, and Gabriel Martinelli, while Manchester United are exploring whether Myles Lewis-Skelly is available. Christian Norgaard is also nearing a £7m transfer to Everton.