No. Serie A registration rules only excluded under the age of 22. Correa is 30, Arnautovic is 35, of course both must be re-register into Serie A list.
Glad you mentioned this, for serie A we could but not of the UCL, it is because Bastoni are counted as homegrown status trained at club by serie A rules.
But obviously it doesn't mean we should register Correa, it could still open for other players.
CT = Club Trained. Trained at club for at least three years between the ages of 15 and 21(UCL). (22 for serie A).
AT = Association Trained. Trained by their club or by another club in the same national association for at least three years between the ages of 15 and 21.
So it registration squad may look like this
Serie A
UCL
Last season, we benefited by Asllani being listed as U-22, which allowed us to register 25 players for serie A but not now. Obviously, we could register a club-trained player such as Carboni to fill the open slot as it suppose to, although, with the recent rumours, it's unlikely now.
Of course, it does not have to be Correa, it could also be reserved for Buchanan when he returns for the next registration, or in the unfortunate event that we are still unable to offload Correa or others such as Satriano, Salcedo, or Agoume.
So the possibility of a new striker means he (or someone else to be sacrificed) is either ready to not be registered for UCL, like Correa was, or he will wait till Arna and Correa leave the club.