Jesus said nothing directly on the issue of homosexuality. There are references to same-gender sexual behavior elsewhere in the New Testament. The most important of these is Romans 1. But, as we have seen, it is not clear that what Paul was concerned about in his context is the same thing we are talking about in ours. There are two other New Testament passages where Paul (or in the case of 1 Timothy, likely someone writing in the spirit of Paul) refer to some sort of same-sex sexual behavior. They are 1 Corinthians 6:9 and 1 Timothy 1:10. A lot of scholarly ink has been spilled regarding just what the Greek words in these verses mean. Rather than rehashing all that myself, I refer you to this written by Evangelical theologian and ethicist, David Gushee:
In 1 Corinthians 6:9 and 1 Timothy 1:10, Paul (in the second case, probably a pseudonymous “Paul”) deploys two “vice lists” — a common enough rhetorical strategy in the Greco-Roman world — to communicate to his readers condemnation of sinful behavior. With regard to 1 Corinthians, most scholars agree that Paul is dealing with an especially unruly congregation, some of whom have fallen prey to moral laxity, including in sexuality. Paul writes to correct that, and to make it perfectly clear that the salvation offered by grace does not also offer an exemption from basic moral requirements. Then follow 10 types of people who, Paul warns, will not “inherit the kingdom of God.” In 1 Timothy 1, the context for the vice list is more obscure. It falls under a discussion of “the law,” and the author’s concern about false teachers apparently focusing overmuch on the law. Paul says that the law is mainly intended for the godless. Then follow seven examples of such godlessness.
In both vice lists the Greek word arsenokoitai is used. In the first list, the word malakoi is directly in front of it. A vast, highly contested scholarly literature exists to parse out the meaning of these two odd little words.