First, please note that we use single as an adjective, eg He is single , not He is a single. As far as I know, you are correct both of "He said he was a single" and "He said he is a single" are right and natural though the tense of the subordinate clause, "he is a single", is not agreed on the tense of the main clause, "He said'. (Of course, what each sentence means are different from each other due to their tenses.
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