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A historical shoujo about Spain and Japan. Maria lives a quiet peaceful life in Spain except for the constant affections of Antonio, but fate changes when Maria trips onto Koujirou, a samurai. (complete)
This is probably the closest you'll get to something like Gosick, without the mystery-solving. Definite romance on both sides.
Popcorn Avatar -
A young boy, saddened and bitter, attempts to take his life. All goes as planned until a foreigner mysteriously appears... (on-going)
Yeah, Lisa, a tsundere with more dere than tsun, definitely likes Kurando from the beginning; and it's obvious that Kurando, a kuudere, cares for Lisa deeply. The above picture is funny only because Kurando is so not his regular kuudere self. Hehe.
Legend Hustle -
Na Hae-Il, whose father works as a scholar, constantly travels around the world, only wants a regular school life. One day, a mysterious white-haired girl appears, claiming that his father sent her. The fourteen-year-old German girl, Tanya, even states that she is Hae-Il's fiancé and ends up pulling Hae-Il into weird situations where men try to kill him. But does Hae-Il have his own powers, and do they come from Tanya? (on-going)
Tanya's a bit of the spoilt tsundere type, but you can tell she likes Hae-Il and he likes her, despite the fact that she spends all his money!
Zen Martial Arts Academy -
Zen is a type of inner power energy that is essential in Marital Arts World and the amount of Zen everyone has is different. Mingyum is person without Zen, who wishes to become East Asia Strongest Martial Artist. Due to his argument with his sister on what Major she wants him to take at school and what he wants, he had left wondering around only to end up in a bad neighbourhood. He ends up saving a girl, but got himself beat up in the process because he has no Zen. Then he got saved by a foreign girl, who announced that she was his fiancée. Now what will happen next? (cancelled)
Definite romance, although awkward at first. It's clear that likes Irene Mingyum, but due to Mingyum's memory loss, he can't remember Irene. But he soon develops feelings for her, regardless of his memory loss. Too bad it was cancelled. :/
Gangsta. -
You wanna get rid of someone? Nicolas and Worick, your neighbourly gangsters, are for hire! (on-going)
The romance is slow-going at this point, but Alex Benedetto (dark-skinned) is very much infatuated with Nicolas Brown (considered Japanese, and it's believed Brown is his adopted name), who is rather awkward around women but seems to have an interest in Alex. (very dark/graphic story)
Ikoku Shoujo to Sumire no Hanataba (Foreign Girl and Bouquet of Violets) -
Masaki Ryou was sent with his older sister to clean up Hiijii-san's mansion. While he was there, Ryou found a water well and accidentally fell into it. As he regained consciousness, he meets this girl named Rose who has been supposedly expecting him, and realizes that he is in pre-modern England. (on-going)
Not sure about the romance on this one yet, as it's hard to say whether Rose likes Masaki or setting him up with Sumire. In either case, Masaki seems to get along with Rose better than Sumire, as the Sumire can be a bit cold and . . . odd (in a good way).
Alyosha -
Foreign exchange student Alyosha Stalina has been attending a Japanese high school for three months. She comes from the nation of Solessia but has yet to fit in with the other students because of her unfriendly demeanour and cold personality. Rightfully so because Alyosha is a trained assassin that has been murdering people since she was five years old. (on-going)
Funny manga. Not much romance, but it's very clear that Asari-kun has a crush on Alyosha, as do a few other boys.
Over Image -
A colourless world, a pure white world, a world where everything is filled with only one colour. What ought to be a young man's usual route to school, Sai is suddenly drawn extraordinary world where he witnesses two young girls fight. One of them is a blonde girl he has never seen before, and the other is Mikage Mikuro, a senpai at his Highschool. After the ordeal, the blonde girl appears as a transfer student at his school. In order to grant her wish, she joined the battle game "Over Image" on her own, and now she seem to have come to sought out Sai to be her companion. (on-going)
The main girl has a mouthful of a name - Miriabilica Staccato - but she's a foreign exchange student and a cross between a tsundere and kuudere, except she doesn't throw a fit like most tsunderes; although she does threaten to kill Sai if he doesn't become her companion. No romance yet, but it's only the first chapter.
I'm sure there are more romance with male Asian protagonist and non-Asian female, but in the realm of made up worlds and kingdoms or outer space, like
Fate/Stay Night, Fate/Zero, Zero no Tsukaima, and
Regelia, etc.
Darker Than Black has both a manga and anime, and though it's not really centred on romance, Hei, who is Chinese, definitely has feelings for Yin, whose Finnish (real name is Kirsikka) and Yin, despite being a doll, develops feelings for Hei. Other than that, I'm afraid the above are the closest to what you're asking for. :/