The Serbia international has failed to live up to expectations since making the move to the Bernabeu from Eintracht Frankfurt in 2019, scoring just two goals in 35 appearances for Los Blancos.
Jovic re-signed to Frankfurt on loan during the 2020-21 campaign before returning to Madrid, but the 23-year-old is not expected to be on the books in the Spanish capital for much longer.
According to Eurosport, Arsenal have taken a liking to Jovic amid uncertainty surrounding Alexandre Lacazette's future, with the Frenchman in the final year of his Emirates deal.
However, the report adds that West Ham United are also in the race, while Jovic himself would likely snub interest from the Premier League in order to return to Germany or sign for a club in Serie A.
Jovic's contract with Real Madrid does not expire until 2025, but he has only played 21 minutes in the current La Liga campaign so far.