Reports in Italy have suggested the Gunners are willing to offer €55 million plus Lucas Torreira in a bid to land the Serbian forward, who has 18 months remaining on his current contract.
Sources have told ESPN that Arsenal have been monitoring Vlahovic for some time but it is unclear at this stage whether a transfer is a realistic possibility this month.
Arsenal spent around €167m last summer on five new players but when asked whether another big deal was within their capabilities, as rumours persist over Vlahovic, Arteta said: "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.
"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.
"[Technical director] Edu and his team are working very hard as 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," he added.
Arteta said: "We are very, very short [in midfield] at the moment. But to be fair on a player, this cannot be the only argument to try to keep a player -- and a player that has been developed and raised through our academy.
"A player that has been patient in many moments and tried to fulfil his dream. He was very straight with me and I understood the situation and we think it's a good option.
"Obviously we are going to move and we are going to look for options because we are very short there."
Arteta will return to the dugout for Sunday's FA Cup third-round tie at Nottingham Forest after recovering from COVID-19 for a second time.
Several players and backroom staff members have also been forced to isolate and the Spaniard said they were "really short with numbers" prior to a further round of testing and fitness updates tomorrow but they "don't expect different then to play on Sunday."