Despite starting on the bench for both the Community Shield defeat to Manchester City and the Premier League opener against Coventry City, neither Arsenal's coaching staff nor the club's hierarchy have any intention of facilitating his exit, the Spanish outlet reports.
According to Marca, recent speculation over a possible departure has no real substance behind it.
The Basque midfielder, 27, retains the full backing of Mikel Arteta, who last week pointed to squad rotation as the explanation for his omission from the starting XI.
The Arsenal manager appears keen to manage Zubimendi's workload carefully after his effectiveness dipped towards the end of last season, when heavy minutes appeared to take a toll.
"We can't allow that to happen again, and then when we reach the final stretch of the season, he's already played 55 matches. We can't allow that to happen again," Arteta said.
"He now has to think about how to raise his level to repeat what he did last year, but over 11 months. That's it."
Even so, everything suggests that following the recent arrival of Brazilian midfielder Bruno Guimarães, Zubimendi will have to work hard to secure a regular starting spot, given that young academy graduate Myles Lewis-Skelly also enjoys Arteta's complete trust in the middle of the pitch.
Zubimendi joined Arsenal from Real Sociedad last summer for a reported £60million and started 34 Premier League matches during a title-winning debut campaign, only losing his place late in the season when Lewis-Skelly emerged as an alternative during the Champions League run-in. He also won the World Cup with Spain over the summer as Rodri's understudy, having previously starred in the same role during Spain's Euro 2024 triumph.
With Arsenal's midfield now more crowded than at any point during Arteta's tenure, the coming weeks will offer a clearer picture of whether Zubimendi can force his way back into regular contention, or whether his role at the Emirates Stadium is set for a more rotational future.
The uncertainty has been fuelled in part by reports linking Zubimendi with a return to Spain, with speculation over interest from Real Madrid gaining traction after the club missed out on Rodri, who joined Barcelona instead.
Sources close to the Bernabéu reportedly view a move as an opportunity to correct what they consider a missed opportunity from a year ago, though Arsenal have shown no willingness to entertain a sale this window.
Arteta has been public in his praise of Zubimendi's contribution, describing him as one of Arsenal's best performers last season and stressing his continued importance regardless of recent team selections.
The Spaniard remains a trusted deputy for Spain in the same defensive-midfield role once occupied by Rodri, underlining his standing as one of the more accomplished specialists in his position, even if game time at club level has become harder to come by in the short term.