Kostic only arrived in Turin last summer after four successful seasons with Eintracht Frankfurt, which was rounded off by claiming the Europa League crown with the Bundesliga club.
The 30-year-old is highly regarded around Europe for his excellent deliveries from wide areas and set pieces, with eye-catching assists numbers to show for it.
Kostic recorded an astonishing 60 assists in his four years with Frankfurt, and would go on to set up another 11 in his debut season at the Allianz Stadium during 2022-23.
Despite that though, Kostic was given fewer opportunities from the start as the season went on, as Juve slumped to a seventh-placed finish following their 10-point penalty.
Samuel Iling-Junior's late season form saw him challenge Kostic for a starting spot, while Federico Chiesa was also deployed in that rather unfamiliar role for him.
TuttoMercatoWeb claims that a Premier League club are interested in the Serbian international, who Juventus value at £13m.
The report states that clues from sources suggest that Forest are the club who hold interest in Kostic, potentially due to their continued hunt for left wing-back.
Steve Cooper started with Ola Aina in that position at the Emirates on Sunday - another summer arrival from Serie A, after joining from Juve's rivals Torino - but the Nigerian is naturally a right-sided player.
After a glittering spell with Frankfurt though, other German clubs are believed to be interested in bringing Kostic back to the Bundesliga.
Wolfsburg are said to be one of the clubs interested after losing both Jerome Roussillon and Paulo Otavio in the last six months.
Forest had been reportedly pursuing a permanent move for Renan Lodi earlier in the summer, but last season's loanee decided to join Marseille instead with a view of playing Champions League football - but the French club have since been eliminated by Panathinaikos in qualifying.
After the move for the Brazilian fell through, Ismail Jakobs was touted as a possible alternative, but progress has not been made on that move in the past few weeks.
Cooper admitted after the Arsenal defeat that more transfers are on the agenda, and are a must if they want to stay up.
The Forest manager said on Saturday: "We know if we really want to grow, get better and improve in this league, we need to bring some players in. I really hope the club can do that,"
"It doesn't get any tougher than this league. We managed to survive last season. We did it in a certain way. We've got to try to evolve that, but to do that we need to add to the starting team and to the squad." Cooper added.
Forest face Sheffield United at the City Ground on Friday night in the Premier League's weekend opener.