The FC Basel defender has attracted admiring glances from a host of English clubs, with Southampton, Everton, and Sunderland all believed to be monitoring the Austrian international's situation in Switzerland.
Gunners boss Arsene Wenger has been credited with an interest in bringing the centre-back to the Emirates Stadium when the transfer window reopens on July 1, but will face widespread competition for the player's signature.
Dragovic is fast building a reputation as one of the most highly rated young defenders in Europe, after a series of impressive performances for Basel in the Europa League this campaign.
At 22, he still has his best years ahead of him, so the decision on his next choice of club will be important for his continued development, with the opportunity to link-up with Wenger in north London likely to be the biggest draw.
The Arsenal boss is renowned for nurturing promising young talent and will look to convince Dragovic that his long-term future will be best served under his tutelage.
Dragovic has made clear his intention to follow in the footsteps of his fellow countryman Andreas Wiemann, who has also enjoyed a promising campaign in England's top-flight with Aston Villa.
"I regular speak to Andreas, who has told me a lot about how much he enjoys playing in England," he is quoted by The Sun.
"Its competition at the highest level, which is what I'm looking for. The fans are fantastic, and the clubs command a lot of respect around the world."