The Premier League table toppers are looking to strengthen their squad in January as they push for their first league triumph since 2003.
Milinkovic-Savic has been repeatedly linked with a move away from Lazio, with Juventus being credited as strong candidates to snap him up.
There were reports that the Serbian midfielder had already agreed to join the Bianconeri, but Lazio president Claudio Lolito moved swiftly to deny those rumours.
The Biancocelesti have been steadfast in their resolve to keep Milinkovic-Savic at the Stadio Olimpico despite concrete interest from several European clubs.
Lolito reiterated last month that the former Genk man is not for sale while also revealing that a new deal is in the works for the midfielder.
However, speculation linking the 27-year-old with a move away from Lazio have persisted, with reports now suggesting Arsenal are willing to go all the way in their pursuit of the midfield general.
Milinkovic-Savic has been widely regarded as the most complete midfielder in Serie A and has served Lazio well since joining the club in 2015.
Juventus are still interested, but their hopes of signing him have been dashed by the ongoing investigation into the club amid allegations of financial scandal.
Paris Saint-Germain and Manchester United are also interested, but Arsenal are looking to be proactive in their pursuit.
The Gunners are having a season to remember in the Premier League. They went into the international break five points ahead of reigning champions Manchester City.
Arsenal will feel they have what it takes to go the distance this season, and the club are looking to strengthen the squad to make it a reality.
Milinkovic-Savic has already shown his class for Lazio this season, notching up five goals and seven assists in 20 games across all competitions.
He will be a shrewd acquisition if Arsenal are successful in their endeavours.
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