Jesus did speak about homosexuality. He said, "Have you not read that He who created them from the beginning made them MALE and FEMALE, and said, "Therefore a MAN shall leave his FATHER and his MOTHER and hold fast to his WIFE, and the two shall become one flesh (Matthew 19:4-5)." Jesus mentioned father and mother, male and female, and husband and wife being made that way from the beginning by God. It doesn't get any more clear than that.
Aside from that, we don't know a fraction of what Jesus said when He was on earth. John ended his gospel by writing,
"Now there are also many other things that Jesus did. Were every one of them to be written, I suppose that the world itself could not contain the books that would be written (John 21:25)."
Even still, God is the author of the Bible (God, Jesus, and the Holy Spirit being One)--the same Bible that declares homosexuality a sin in Leviticus 18 and 20, Romans 1, 1 Corinthians 6, and 1 Timothy 1.
Besides that, the Gospels were biographies of Jesus, written to show that salvation had come. The epistles were written to teach people how to live. The gospel writers were not as concerned with teaching daily conduct. Paul, however, was. That is why on three occasions he condemned homosexuality.
Finally, the Bible says all Scripture is profitable for teaching and instruction in righteousness (2 Timothy 3:16). If a person is really concerned with what Jesus had to say on the topic, then the words of Moses and Paul (inspired by God) should suffice.
So if this man's question is sincere, I would tell him to fill in the blank with:
*It is an abomination (Leviticus 18:22, 20:13)
*It is unnatural (Romans 1:26-27)
*They will not inherit the kingdom of God (1 Corinthians 6:9-10)
*It goes against sound teaching (1 Timothy 6:9-10)
This list, quite honestly, can be said about almost any sin. Whether heterosexual or homosexual, all sin needs to be repented of. Jesus said that if we really want to follow Him, we need to deny ourselves; this includes the lusts of the flesh, the lusts of the eyes, and the pride of life.