The 28-year-old central defender is surplus to requirements at the Emirates Stadium this season, having spent the second half of last year on loan at Udinese.
Now Mari is set to return to Serie A with newly-promoted Monza, with only the finer details of the loan to be agreed between the clubs.
It is understood the inclusion of an option in the deal for Monza to make the switch permanent is the only stumbling block that remains, potentially because relegation back to Serie B would mean the club would not have the finances to complete the transfer.
Another player closing in on a move away from north London is goalkeeper Alex Runarsson.
It is understood two Turkish clubs are interested in a permanent deal for the Iceland international, who has made just six first-team appearances since joining the Gunners in 2020.
Having already signed Fabio Vieira, Marquinhos, Matt Turner, Gabriel Jesus and Oleksandr Zinchenko this summer, any other additions are likely to rely on Arsenal clearing more money off the wage bill.
Hector Bellerin looks likely to join Real Betis, where he spent last season on loan, but Arsenal are keen not to terminate his contract even though they do not want to stand in his way of securing a move.
Mikel Arteta, whose side opened their Premier League account with a 2-0 win at Crystal Palace on Friday night, is also understood to be willing to listen to loan offers for both Ainsley Maitland-Niles and Reiss Nelson.
In terms of recruitment, Leicester midfielder Youri Tielemans continues to be linked with a switch to the Emirates but it is believed that no deal has yet to be discussed between the two clubs.