The former Eintracht Frankfurt striker has flattered to deceive at the Bernabeu over the past three years and has been expected to seek pastures new in the current window.
Jovic cost Los Blancos £56.7m to prise away from the Deutsche Bank Park in the summer of 2019, but he has only found the back of the net three times for Real in 51 appearances.
Frankfurt welcomed Jovic back on loan for a brief period in the 2020-21 season, and the 24-year-old was only handed one start by Carlo Ancelotti in the 2021-22 La Liga campaign.
Fiorentina - who lost Jovic's Serbia teammate Dusan Vlahovic to Juventus in January - are now said to be closing in on the temporary signing of Jovic, according to Sky Italia.
The report claims that Jovic will arrive at La Viola on a straight loan with no option or obligation to buy, and the two clubs held "very positive" talks over a deal on Tuesday.
The Serbia international should therefore be announced as a Fiorentina player next week, and Real Madrid will continue to pay half of his €6m (£5.2m) yearly salary.
Jovic is not due to become a free agent until the summer of 2025, and the forward has won the Champions League, two La Liga titles and two Supercopa de Espana crowns at the Bernabeu.
However, Jovic only earned 113 minutes of action in Real's recent continental campaign and did not play a single game in the knockout rounds, as Ancelotti left him out of the squad for the final win over Liverpool.
Jovic found it difficult to make his mark over the prolific Karim Benzema, whom Real Madrid are supposedly confident of agreeing a contract extension with beyond the summer of 2023.
Neither Kylian Mbappe nor Erling Braut Haaland will be lining up at the Bernabeu next term, but Ancelotti could still be prepared to part ways with two of his fringe strikers.
As well as Jovic, the out-of-favour Mariano Diaz has allegedly informed Real of his desire to leave the club this summer after making just 11 appearances across all competitions last term.
Marcelo, Isco and Gareth Bale have all left the Spanish and European champions on free transfers, and the likes of Jovic, Diaz, Marco Asensio and Dani Ceballos could follow before the window shuts.
Aurelien Tchouameni and Antonio Rudiger have both arrived at the club from Monaco and Chelsea respectively, and president Florentino Perez has admitted that his side are unlikely to make any more signings this summer.