The 27-year-old enjoyed another fine campaign, scoring four goals and tallying 11 assists, having contributed 10 goals and 13 assists across all competitions last season.
Bobic was asked about the future of Kostic and he said: "Filip is happy here. He feels very comfortable with us, but it may also be that we are ready to release him.
"That depends not only on us, but also on the player. But I can imagine that he will play here next season: fans happy, players happy, me happy."
Bobic, who sanctioned the big-money departures of Luka Jovic (Real Madrid) and Sebastien Haller (West Ham) at the start of the season as Eintracht made significant profits, is anticipating a difficult transfer period due to the Covid-19 crisis.
"The goal was clearly to break the €300 million mark in the 2019-20 season," he said. "But suddenly there was a stop sign at €280m."
"There are an incredible number of players on offer right now, including interesting ones. But we have to look at the books to see what is possible. Because we do not know how long the situation will last.
"We have to be patient, it will be tough and long. It won't be an easy time. We already have a few players we would like to sign but if the money is not there, you cannot buy."
Bobic – who is also planning to offer head coach Adi Hutter a new contract – was also asked about Ante Rebic and loanee Andre Silva.
Rebic joined Milan on a two-year loan deal at the start of the season as Silva moved to Eintracht on the same terms.
Milan are reportedly keen on signing Rebic permanently, while Silva scored 16 goals for Eintracht.
"We have agreed with the owner of Milan that we will get together soon and talk about the topic," Bobic said. "I don't think Ante wants to get back to our salary level.
"Andre knows that we are happy with him. He is also happy to be here in Frankfurt and can imagine staying longer."