The Serbian teenager is also attracting interest from three clubs on the continent and has been likened to Zlatan Ibrahimovic.
And the quartet could apparently miss out entirely if Real Madrid show an interest, with Vlahovic previously speaking of his desire to play for Los Blancos.
Vlahovic, who is already 6ft 2, has drawn comparisons with PSG talisman Zlatan Ibrahimovic, a player also being linked with a move to England.
The Serbian has played six times for Partizan in total and became the youngest player in club history upon making his debut in February.
With Arsenal's Olivier Giroud fast approaching his thirties, it makes sense for the Gunners to be seeking out more youthful alternatives - especially ones of Vlahovic's frame.
City, meanwhile, don't currently possess a player like Vlahovic at senior level, having sod Edin Dzeko to Roma last summer.
One of the youngster's teammates at the Partizan Stadium is former City striker Valeri Bojinov, who's scored 13 goals in 22 league appearances this season.