He said that he loved her: this is simply reporting what he said. Another way of saying the same thing is: He said "I love you". Here,.the speaking very clearly happened in the past, and it referred to love in that past time. This is the normal way of reporting speech, and probably what your grammar book is expecting.
Unlike your previous question, which worked equally well in past and present, it's hard to imagine a valid use for 'love' in the present here, maybe "I just saw Fred hit Jean, but he SAID he loves her" - the focus is on the present, as I am contrasting his behaviour with the idea that he loves her. This is quite an advanced usage, probably above the level of your book.
If you have to take an exam based on the rules in the book, learn them, you can worry about learning English for real once you've got your certificate :-)