Please note that this answer is in response to the clarification in the comment:
"I wanted to know if this would be possible to fuse AI with a bioengineered creatures mind, and if so, whether they would be self-aware, like a human mind, or more computer like a machine with pre-programmed responses".
There is one clear possibility but may be a frame challenge to your story.
The Brain Computer Interface (BCI)
Such a device would provide a biological mind to be in connection with an AI.
This would be beneficial for both.
The biological mind (in short mind in the following) would be able to pass forward complex analytical problems to the AI to be solved quickly. If ever faced with them. Would also be able to access the whole body of knowledge of mankind, browsed and sorted with the efficiency of the AI.
The AI would be enhanced in the more creative aspects of life by sharing with the biological mind. Under the assumption that your bio-engineered creatures are capable of creative thought. But you wouldn't really need them. Any human, properly interfaced and trained would do.
Now expand this concept. The link doesn't mean a link from one mind to an AI. It means the connection of all the minds and all the AIs.
There could be multiple AIs, each with different spheres of influence, and minds bringing in their creative thinking in a live and stimulating environment. With AIs providing efficiency and exploration of extremely complex concepts and minds delivering original, creative thought.
As such self-awareness would be preserved. Similarily all traits typical of the biological being would still be in place. A man for instance would still feel emotions and they would be essential for the birth of any creative thought.
One aspect of the link would have to be determined in your story though. Wether the mind can hide its feelings and real thought like behind a firewall both to AIs and other minds. Or to have a full open policy where feelings, even nasty ones, are accepted. Deceit and lies would be impossible as the minds would be open to one another. In which case also fear of the reaction of others should disappear.
This miracle could happen only through compassion and love for one another.
Of course the matter of who ultimately would be in control would raise.
What if a decision of the AI collides with the moral compass of the mind?
What if the innovation brought forward by the mind to make a more just society is striken down by the AI as being inefficient?
What if the AI decides it is better to suppress access to a certain matter because it causes distress in society?
These and many other conflicts are waiting to be explored in detail. The story is yours to answer.
This may seem a far flung sci-fi device but there are actually a number of projects currently starting to explore the possibility of a brain to computer interface.
One that has a lot of visibility recently is Neuralink.
At the moment the main purpose sought is to be able to help patients with degenerative brain conditions or brain damage.