Could someone tell me which modal verbs are used for reporting speech or thought? I'd appreciate an example.
All of them, I think. Example: "He might have said hello".

Or have I misunderstood the quesion?
I don't really understand the question either...

Konstantin, you're referring to the Conditional with your German example.
Indirect speech in German works differently as the Conjunctive has to be used in formal German, which however, can be replaced by the Conditional (would+infinitive).

In English, the tenses have to be shiftes back from direct to indirect speech - .... but NOW - that I've been thinking about this, I might have got an idea of what maj's question aimed at:

The modals "can" and "may" only occur in their forms in simple present and simple past tense, "must" is used in simple present tense only. Now, if you have a sentence including one of these modals, that need to be shifted back, you've to use substitute forms for all of these three modal helping verbs:

Linda: "He can speak English" -------- Linda said he "was able to" (could) speak English.
Linda: "He could speak English" ------ Linda said he "had been able to" speak English.

Linda: "He may go" -------------------- Linda said he "was allowed to" (might) go.
Linda: "He might go" ------------------ Linda said he "had been allowed to" go.

Linda: "He must leave" ----------------- Linda said he "had to" leave.
Linda: "He had to leave" --------------- Linda said he "had had to" leave.

("might" and "could" are commonly usually used as conjunctive forms though, but can express past tense also)

As you can see in these examples, some modals cannot appear in their own forms in special indirect sentences, so maybe that was the problem, maj was aiming at?!

Hope I could help... Emotion: smile
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Although I'm unable to answer the question, I think it can define it more precisely.
Is about with the help of which modal verbs you can tell what another person said.
They have it in German and that is, I think, what the question means - whether there is such a construction in English.
For example:
Direct speech: "I am tired", said the teacher.
Indirect speech would be: The teacher said he WOULD be tired.
I am not sure whether WOULD is correct at this place but I hope the question is more understandable now. The answer would be interesting to me.
Thanks all for answers!
"The teacher said he would be tired" is perfectly okay in English. I don't know whether or not this is specifically related to reported speech, however. This is an example of "future in past" tense - describing a prediction made in the past.

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 Pemmican's reply was promoted to an answer.