Do you u agree that can be both, with or without 'that'?
Isn't better keep the word 'that' in the second sentence so as to look like with the original sentence?
Diego, my (partial) fault. The first sentence isn't the same as the second one, as with the proper punctuation, the first one would read
He said: "I love you".
But in the second one, the word "that" should be indeed suppressed because it is only kept when actually needed for the sentence structure. In English, one would simply say "He said he loved you".
As Goncin said there should be a proper punctuation, but the first sentence should read:
S/he said "I love you".
We have this sentence into 3ª person "dijo" not "dije".
For the second sentence it should read:
He said he loved you.
This is a case of typical "reported speech"
You must match the verb tenses either "he says he loves you" or "He said he loved you"