This is just an educated opinion, but no, they can't be sued. And they can, maybe, with some creative interpretation of caselaw.
It goes directly to his work contract. The contract stipulates the term he's employed by Frankfurt and his contractual obligations. Unless there is a release clause in the contract, the club has no legal responsibility to sell the player.
Filip Kostic could risk being in breach of his own contract if he does not show up for practice - This is at the discretion of the club if they wish to pursue penalties such as fines if the player refuses to train.
That's the formalities. A "promise to sell" is just that, a promise.
On that note... Here is how they COULD be sued.
German contract law is similar to most other European contract laws but reads as follows:
Unless the law provides otherwise, oral contracts are generally valid and may be proved by any type of evidence. However, certain contracts must be in writing; the most important
of these include:
1. The inter vivos establishment of a foundation;
2. Assuming or assigning a mortgage;
3. A lease for more than one year;
4. A promise of an annuity;
5. Guaranty and surety contracts (unless the transaction
is a commercial one for the guarantor or surety);
6. A promise to payor perform which is independent of
and unrelated to any other obligation (Schuldversprechen);l0
and
7. Acknowledgment of a debt (Schuldanerkenntis).
None of pt. 1-7 directlly contradicts the premise of selling a football player between clubs for a fixed fee. The argument any legal action form Kostic's side would have to prove that the club has in fact made a verbal agreement with Kostic to sell him at the reported price. As the price has been both reported online, and further evidence provided by the clubs own subterfuge,
could provide a sufficient argument that Frankfurt has broken a verbal contract. The adversary’s party may fully or partially deny entering into an oral contract, whereas its up to the plaintiff to prove that it hs in fact done so. I've been unable to find a comparable case in CAS, which is where this argument would be heard, as opposed to a German court. I listed the contract law from Germany since its applicable even in CAS.
Penalties for Frankfurt could range between anything from: Allowing the player to complete the transfer to the bidding club AFTER the transfer deadline (this won't happen, theres no time to conclude a case like this in time for the next available transfer deadline, even the January window and would have to involve UEFA), fining Frankfurt, UEFA can choose to ban the club from European competition, etc.. Or there is no penalty at all. There's no presedence here, I can't recall a club flat out
lying to a player like this. Everything is just an educated guess and possibility before someone takes legal action.
It's equally possible that the club can prove that it has not entered in a verbal contract and that it reserves the right to refuse an offer even if it matches the reported price. Sales are completely at the disecrtion of the selling club. The only thing that makes this interesting is the part where they hide a bid from the player. Which is so weird.
But man, this is some teenage highschool dramaclub fanfiction. Whoever dictates transfer operations at Frankfurt has the moral backbone of a very moist jellyfish.
Instead of acting like an adult and telling the player "We don't want to sell you, see you on Monday", the club instead offers the player at a marketprice thats reasonable to a buying club and gives the player false hope and expectations. This ranks right up there with Arteta in future academy lectures on: "How not to deal with problems that arises in a football club".