A little innovation that shouldn't be too difficult to implement.
It would be nice to be able to indicate that a player is not transferable by ticking a tab, for example.
I have to admit that when I'm looking for a very specific profile, I probably end up asking managers several times who have said no to me in the past. Ceal can be annoying, I agree. That's why this small improvement could be beneficial for everyone.
What do you think?

Not necessarily for
I'll give you my opinion: sometimes I'm looking for a player because I need to strengthen the team quickly. The players at auction or on the list are not necessarily the only way and it is possible that the profile sought does not correspond to me, in this case I seek a profile and if it is not on the list of transfers and I make an offer (of course suitable) free then with the club receiving the offer to accept it or not
Perso j'y ai mis le prix car comme expliqué je voulais recruter et j'ai peut être payer cher mais au moins je l'ai eu tout de suite et on était tous les deux satisfaits 😃

Mais pour les offres vraiment abusive sur des joueurs qui en valent bien plus

The non-transferable option is called the counter-offer.
Don't worry, if you ask for 500M for a player you don't want to sell, he'll never leave you (and even if the opposing coach recruits him, he'll come back to you under the transfer rules ^^)