Well, mostly Jesus’ romantic feelings would be for His Bride the Church. There’s an awful lot of “eager bridegroom” stuff in early Christian literature, and it’s all about His Second Coming as hurrying to the wedding, running like a giant and pitching his wedding tent in the Sun. (This being a lot more cheerful image than “Jesus comes back to judge everybody and let everybody know everything everybody has ever done, and then throws some people into Hell.”)
So if you want to postulate a romantic relationship, you’re postulating St. Mary Magdalene being dumped for another Woman who’s sinless and eternal, and of whom St. Mary M is one tiny little cell or body part, and anyway is a personification of Christ’s Own Body.
(It’s so mysterious a part of the story of God the Trinity that it’s not at all easy to picture, and there’s plenty of ways to make it sound nasty – probably heretical too. So it’s probably better not even to try to drag in third parties…)
Romance is just a pale human shadow of God’s total love for everything. That’s not to say anything against romance, anymore than I would say anything against a little tiny pond or creek. They’re important to birds and plants and animals, and worthy of respect. But God is Love, and God’s love is like the entirety of water in the world and the universe.
If Jesus did have specific romantic interest in anybody on Earth, it was probably somebody from His village whom we’ve never heard of. But given how eager He was to finish His mission and get salvation done, I think it really is His Bride whom He loves and always loved.
The thing about romance is that it naturally fixes one’s total being on one single person, forsaking romantic love for all others. If Jesus had ever done that in a romantic way at anybody, there’s a serious possibility that the entire universe would have fallen apart and faded away. So nooooo, not thinking it’s a good plan, except in the way of the big salvation history plan with the Bride, in a new and more robust Creation.
But just to entertain you… the older (medieval, anyway) romantic notion/legend about St. Mary M was that she (and/or St. Mary of Bethany, and/or the woman who was caught in adultery, and/or the sinful woman who washed Jesus’ feet) and St. John were the couple at Cana, and that St. John left her behind like a dirty shirt to follow Jesus, which led her to pursue a life of sin and seven-demon-possession from which Jesus had to come pull her out. And this version didn’t include any happy endings for her with her ex-boyfriend St. John or anybody else, so it’s another downer from that point of view. (And I don’t think of St. John as that kind of guy at all. Kind of insulting to him.) Medieval literature is full of this kind of stuff, though, if it’s the kind of stuff you like. (Judas’ mean girlfriend who stole all the money was really the one to blame, of course. Heh.)
It’s a lot better to focus on St Mary M getting to carry the good news of the Resurrection first of all, as a reward for her faithful friendship. (And seeing that she was in roughly the same position as Christ’s aunts and cousins, Jesus thinking of her as a sort of adopted aunt or cousin or friend or student seems more likely.)