Reports in Italy claim Arsenal have made the first move for Vlahovic with a player-plus-cash offer for a striker admired by many of Europe's elite.
The Serbian hotshot equalled Cristiano Ronaldo's record of 33 Serie A goals in a calendar year during 2021, and has since been linked to Tottenham, Juventus and Barcelona among others.
Arteta's Arsenal are facing plenty of uncertainty in their striker positions, with Pierre-Emerick Aubameyang dropped and stripped of the captaincy, while Alexandre Lacazette's contract expires in the summer.
And now, according to Gazzetta dello Sport, Arsenal have offered £43m plus Lucas Torreira for the frontman.
Vlahovic is among a number of linked solutions, including the likes of Alexander Isak and Dominic Calvert-Lewin, and amid reports of a move for the Fiorentina man, Arteta has pushed his side to keep spending.
"I think with the amount of things and the way that we want to evolve the squad, we have to maximise every window in many different ways and we are alert," the Spaniard said.
"[Technical director] Edu and his team are working very hard because we know exactly what we need to do, and whether we can accomplish that in January or in the summer, is a different question as it is related to other stuff.
Arsenal spent the most money of any Premier League side during the summer, shedding out over £150m on the likes of Ben White, Martin Odegaaed and Aaron Ramsdale.
The Gunners now look set to challenge for a return to the Champions League for the first time since Arsene Wenger left the club, currently sitting in fourth place with two more games played than rivals Tottenham two points back.
Many of Arteta's signings since becoming Arsenal manager in 2019 have begun to pay off though, with the likes of Ramsdale and Takehiro Tomiyasu receiving praise.
And Arteta is now backing his owners to try and continue the upward trend, particularly in the winter window.
"If it is the right player and we can afford it and we can do what we want to do we will discuss it and make the best possible decision. We are open [to doing business this month]."
Arsenal are set to have even more space in their forward positions, with highly-rated youngster Falorin Balogun set to complete a loan move to Middlesbrough, while Eddie Nketiah is attracting strong interest from German side Borussia Monchengladbach.