Mixing present and past tense in a report or public announcement
Solution 1:
Both are correct and whether you use the former or the latter depends solely on whether the implications of the statement are still valid today or were valid only in the past. With that said, consider the following:
Jane tried to explain that John was really sick. It's a shame nobody believed her. Now that he's dead, it doesn't even matter anymore.
versus
Jane tried to explain that John is really sick. I think we should visit him and find out for ourselves; what if he needs medical attention?
The same rule applies to negatives.
Solution 2:
What did she say? She said Michael is a suspect. When speech is reported it becomes indirect speech and indirect speech requires adjustments to the verbs. Where the verb in the speech as spoken is in the present tense, it goes into the past tense when reported. So, She said Michael was a suspect or, in this case, She made a statement that Michael was a suspect. If she had said Michael isn’t a suspect the verb in the present tense would still go into the past tense: She made a statement that Michael wasn’t a suspect. She didn’t make a statement that Michael was a suspect means something different, but the verb is still was and not is. (I’ve changed never made to didn’t make because, although never is found as the normal negator in some dialects, in Standard English it is only used to mean ‘at no time’.)
Solution 3:
Barrie and Rimmer are both partially right. The default tense for reported speech is the past tense. By switching it to the present tense, you are signaling that the statement is still true. So
She said Michael is a suspect.
means that Michael is still a suspect. But
She said Michael was a suspect.
doesn't tell you whether or not Michael is still a suspect.
UPDATE: this may differ in British and American English. If you do an Ngram comparing "He said she was" and "He said she is", you find a very small fraction of occurrences of "He said she is" if you specify American English, but none if you specify British English. On the other hand, if you look at the actual hits, the results of this Ngram look pretty untrustworthy.
But even in American English, you would say "She said Michael was a suspect" unless you're specifically (possibly without realizing it) calling attention to the fact that Michael still is a suspect. And the results of Google search for phrases like "He said she is" turn up some instances where people are indeed doing this.