The 24-year-old has been heavily linked with a move away from Real Sociedad over the last 18 months, with Barcelona, Manchester United and Arsenal all said to be keen on the Spain international.
Zubimendi has a contract with his Basque side until June 2027, but his release clause is believed to be as low as €50m (£43.6m), and according to Sport, Arsenal are considering activating the buy-out fee to sign him before the end of the winter market.
The report claims that the Gunners are willing to meet the release clause, with Real Sociedad signalling that he would not be allowed to leave for less.
The midfielder has scored four times and registered one assist in 28 appearances for his Basque club during the 2023-24 campaign, including four goals and one assist in 19 La Liga outings.
Zubimendi came through the youth system at Real Sociedad before making his first-team debut in 2019, and he has now turned out for the club on 171 occasions, scoring eight times and registering seven assists.
Arsenal head coach Mikel Arteta is believed to want to bring in a midfielder capable of playing in a two with Declan Rice, with Zubimendi seemingly being identified as the leading target.
Real Sociedad will be desperate to keep hold of the midfielder for at least the rest of the season, but the presence of the release clause leaves them in a difficult position.
Arsenal also continue to be linked with a possible forward addition, with Ivan Toney thought to have been their leading target, but the Englishman is now expected to stay with Brentford until the summer.
The Gunners have also been credited with an interest in Getafe's Borja Mayoral, with the North London outfit believed to have had a £22m bid for him rejected by the capital outfit.
Eddie Nketiah is being linked with an exit, with Crystal Palace said to be interested, although he will not be allowed to leave the club unless a replacement is signed.
Wolverhampton Wanderers attacker Pedro Neto is another player being linked with a switch to the Emirates Stadium during the January transfer window.
Arsenal are currently on a run of three straight losses, and they will be bidding to return to winning ways when they welcome Crystal Palace to the Emirates Stadium in the Premier League on January 20.