The 22-year-old only arrived at San Siro from Brescia in 2020 - initially on loan - and he made his switch to the Scudetto holders permanent for their triumphant 2021-22 season.
Competing with Franck Kessie and Ismael Bennacer for starts in Stefano Pioli's double pivot, Tonali was a standout performer for the Rossoneri last term with five goals and three assists in 36 Serie A games.
Tonali has since broken into Roberto Mancini's Italy squad amid his strong form at club level, and he remains under contract at San Siro for another four years.
However, there were rumours that Arsenal were prepared to try their luck with a £40m bid for Tonali, who missed Saturday's opening Serie A win over Udinese due to a groin injury.
The Gunners will seemingly be forced to look elsewhere in their search for midfield reinforcements, though, as Tonali has confirmed his desire to stay on with the Italian champions.
"[Joining AC Milan] was the right thing to do and my development has been a natural consequence," Tonali said in an interview with Sette Magazine, as quoted by the Evening Standard.
"Being in a team permanently is not like being out on loan. It's a detail that alone counts little, but makes the difference by adding other factors. If you play badly while on loan, you can be worried the club won't sign you. I joined Milan at the right moment and I want to stay."
Tonali has already made 82 appearances in all tournaments for the Rossoneri, with Bennacer and Rade Krunic featuring in the midfield on Saturday in his absence.
Arsenal have therefore been dealt a minor blow in their pursuit of further summer acquisitions, with Mikel Arteta affirming that his side are still open for business in the coming weeks.
Leicester City's Youri Tielemans is believed to have been a prime target for Arsenal for a number of weeks now, and Gunners fans addressed the Belgian with transfer-related chants in Saturday's 4-2 Premier League win over the Foxes.
However, Leicester are thought to be demanding in excess of £30m for the 25-year-old, who is out of contract at the end of the season, and Arsenal could therefore try to sign him on a free transfer in 2023 instead.
Coincidentally, Milan have been tipped to move for one of Arsenal's lynchpins in Albert Sambi Lokonga, who has struggled to displace the perennial pairing of Granit Xhaka and Thomas Partey.
Lokonga - who started 12 Premier League games last term - only came off the bench for the final minute of last Friday's 2-0 win over Crystal Palace and was an unused substitute in the win over Leicester.
Nevertheless, the 22-year-old reportedly has no interest in heading for the Emirates exit door amid links with Milan and feels that Arsenal is still the best place for him to develop.