According to this link, the verb tense in the subordinate clause can be either present or past tense when the main clause's verb is in past tense IF the fact stated in the subordinate clause still holds true. The linked article clarifies the point by claiming that the sentence (1)
He said, "I like coffee." (1)
can be changed into either (2a) or (2b) if his liking for coffee is still strong:
He said (that) he liked coffee. (2a)
He said (that) he likes coffee. (2b)
Then it hit me that whether this optionality can be applied or not to the following case, namely, where the verb in the main clause is in past tense in the negative form:
He didn't say, "I like coffee." (3)
I'm not sure if (4a) and (4b) are both acceptable ways to express the same idea of (3) given that he likes coffee at the present time.
He didn't say he liked coffee. (4a)
He didn't say he likes coffee. (4b)
To eliminate the possible confusion caused by the vagueness of the sentences (4a)/(4b), let's assume that the stress falls on the second word: "He didn't say he liked/likes coffee."