However, a bid of over £45million from the Gunners could warm up the San Siro giants to a possible move, according to reports in the Italian media.
Italian journalist Enrico Camelio claims Arsenal and Milan have already met to discuss the possible transfer of Tonali.
"Milan and Arsenal met and talked about Tonali," said Camelio. "The Rossoneri have declared that the midfielder is not transferable, but if a proposal for €55m arrives, Milan could sell him and make two purchases".
However, the Italian international is already part of the furniture at the San Siro, despite only arriving last season from Brescia last summer on a permanent deal.
He also spent the 2020/21 at AC Milan on loan from Brescia and has scored six goals in 96 Serie A appearances across both clubs.
Arsenal have already made five signings this season with Gabriel Jesus, Oleksandr Zinchenko, Fabio Vieira, Matt Turner, and Marquinhos all joining the club.
They are still in hot pursuit of Leicester midfielder Youri Tielemans, though little movement has been made on that transfer so far.