A suspect does not have to suspected of a crime—although that is often its usage—but simply of something.
From Merriam-Webster's definition of suspect:
: one that is suspected
especially : a person suspected of a crime
For example, an anonymous letter is sent to a group of people. This letter says that a crime will be committed. Police could start an investigation into who sent this letter. Even though no actual crime has been committed (assuming that sending such a letter is not itself a crime), the police could still find suspects for the act of having written the letter.
Similarly, in a large family, numerous people could be suspected of having written a strange symbol on a whiteboard. Nobody in the family admits to having done it. But there are certain family members who could be considered suspects. Writing on a whiteboard is not a crime but there are still suspects involved in the non-criminal activity.
A suspect does need to be suspected of something concrete.
If I am psychic and I foresee future events, and I foresee somebody being murdered tomorrow morning—but I don't see who—I could conceivably put together a list of suspects. The police would almost certainly never believe me on the basis of my vision. (Although in some fictional movies and books, somebody known to always be right could be taken seriously.) Nor would other people who I told about this. So, to everybody else, it's unlikely that this future event would be believed; therefore, nobody would be considered a suspect. But as far as I was concerned, I could investigate and come up with a list of suspects.
In this scenario, it's enough that I believe it—and so I can use the word, even if other people wouldn't.
Even in the case of already committed actions, it's possible for different people to have a different list of suspects. Detective A might think that person A is a suspect, but detective B doesn't think so. So, in that sense, who is a suspect could be considered subjective.
In the example in your question, the detective must have a reason for believing that the person will commit a future crime. Most likely, this is because the person is already a suspect for having committed crimes in the past. But let's say it's known they committed past crimes—and were convicted and jailed for them. They have just been released from jail. This detective now believes that they will offend again. In this case, the status of the person as suspect is similar to the scenario of the psychic with a vision about the future. To the detective, the person is a suspect. But to other people that wouldn't necessarily be the case.
I would say that to those other people—who don't feel convinced that the murderer will commit another crime—this person would be considered a person of interest rather than an actual suspect:
: a person who is believed to be possibly involved in a crime but has not been charged or arrested
Even though this term is also normally used for crimes that have already happened, it could be more easily applied to probable future crimes than could the more certain suspect. It just means somebody to watch and consider—until further evidence is gathered. (In this case, until a crime is actually committed or attempted.)