In the following, Bellarmine, notwithstanding holding to an Amillennial eschatology, defends the thesis that the Bible predicts a future coming of Elijah, and that such prophecies were not fulfilled [at least fully] in the person of John the Baptist; for more, see my post: Refuting the Tanners on the LDS Interpretation of Malachi 4:5-6:
But to us it does not seem to be childish imagination, but a true statement—that Enoch and Elijah will come in their own persons, and that the contrary is either a heresy or an error proximate to heresy, and this is proved first of all from those four Scripture texts [Mal 4:5; Sirach 48:9-10; Rev 11:3; Matt 11:14]. For, that Malachi’s words cannot be understood to be about some teachers, like Luther, Zwingli, and others like them, is clear; for, Malachi says that the Jews will be converted by Elijah, and that he is to be sent especially for the sake of the Jews, as is clear from this: I will send to you, and from Sirach: To restore the tribes of Jacob; but Luther and Zwingli did not convert any Jews.
Also, that these words cannot be understood to be about John the Baptist literally but only about Elijah is clear, because Malachi is speaking about the second coming of the Lord, which will be for judgment, for he says this: Before the great and terrible day of the Lord comes. For, the first coming is not called the great and terrible day, but the acceptable time, the day of salvation, hence also he adds: Lest I come and smite the land with a curse, that is, lest coming for judgement and finding all the wicked, I condemn all the earth. Therefore, I will send Elijah so that I may have some whom I will save. But the first coming the Lord came not to judge; but to be judged; not to condemn, but to save . . . Now it will be proved that Sirach also is speaking about the persons themselves of Henoch and Elijah, not about some persons. For, Sirach says that Enoch will come to give repentance to the Gentiles, and he was taken up into paradise; and that Elijah will come to restore the tribes of Israel, who was taken up by a whirlwind of fire, in a chariot of horses of fire; these things certainly pertain only to these particular persons . . . Now it is evident that the words of the Lord in Matt. 17 are to be understood about the true Elijah, not about John the Baptist, because John had already come, and finished his course, and still the Lord says: Elijah will come. But it can be proved that these words are not to be understood about all teachers, but about the one true Elijah. First, because the apostles who raised the question about Elijah were Peter, James and John, and they took the occasion from the Transfiguration of the Lord, where they saw Moses and Elijah. Therefore when they ask: Why do the scribes say that first Elijah must come?, they are speaking about the Elijah whom they had seen on the mountain with Christ. Therefore Christ is responding, Elijah indeed will come, and he will restore all things, is also speaking about that particular Elijah, who appeared at the transfiguration. Secondly, the same thing is clear from the words, and he will restore all things. For, John the Baptist did not do that, nor did any other person. For, to restore all things is to recall all Jews, and heretics, and perhaps many Catholics deceived by the Antichrist back to the true faith.
But Bibliander objects, because the Lord in Matt. 11 says about John the Baptist, he is Elijah who is to come, as if he were to say: He is Elijah promised by Malachi. I respond that the Lord wants to say that John was the promised Elijah, not literally, but allegorically; for he said just before that, if you are willing to accept it, as if he were to wish to have an Elijah for the first coming, accept John. Therefore also he added: He who has ears to hear, let him hear, indicating that what he had said was a mystery, namely, that John was Elijah. (Robert Bellarmine, Controversies of the Christian Faith [trans. Kenneth Baker; Keep The Faith, 2016], 868-69)