The 27-year-old has long been linked with a move to a host of Europe's top clubs, but no move has yet materialised to date, leaving him to enjoy a successful seven-year period in Rome so far.
The Gunners are said to be interested in strengthening their midfield this summer, with the likes of Leicester City's Youri Tielemans being heavily linked with a move to the Emirates Stadium.
Wolverhampton Wanderers' Ruben Neves has also been considered, but Corriere dello Sport are reporting that Mikel Arteta is said to be readying an offer for Milinkovic-Savic during the current transfer window.
The report also outlines apparent interest from fellow Premier League side Newcastle United, but that the midfielder is set to snub interest from the duo due to his interest in joining a 'top' side instead.
Regardless, Arsenal are set to bid around £42m for Milinkovic-Savic according to the report, but Lazio are said to be holding out for a fee of around £55m for their player, who has two years left to run on his deal with the Serie A side.
Milinkovic-Savic could well be a potential replacement for Granit Xhaka in North London, who is said to be attracting interest from Jose Mourinho's Roma once again, following a failed move last summer.