Self-Proclaimed Love Interest

A Comedy Trope where one character claims that they are someone else's one-and-only true love (and vice-versa), even though the two are not actually in love, dating, or (in extreme cases) even anything more than casual acquaintances. This character may exhibit traits of Stalker with a Crush, although they will deny that they are any such thing. They will also become a Green-Eyed Monster if they see their "boyfriend/girlfriend" anywhere near another boy/girl, even though they have no legitimate claim to the person. For maximum comedy, the object of their "love" may find themself dragged out on a date against their will.

When seen outside of comedy, this character can be bad news, as it's usually indicative of serious issues of some sort.

Can be Truth in Television. The psychological disorder Erotomania causes an extreme manifestation of this trope wherein the afflicted individual comes to believe that a specific person is in love with him/her and acts based on that belief. The fixation can be triggered by something as innocent as a smile from the person as they pass the afflicted individual on the street.

Compare Abhorrent Admirer, Clingy Jealous Girl and Stalker with a Crush. Contrast She Is Not My Girlfriend. Also, this kind of behavior is typical of the Yandere.

Examples of Self-Proclaimed Love Interest include:

Anime and Manga

Tokiwa from Ask Dr. Rin! plays this trope for drama while he's posessed.
Nodame from Nodame Cantabile, so much. She actually declares herself Chiaki's wife, and some people take her seriously, but they aren't even dating or anything and Chiaki mostly thinks of her as a pest outside of being a genius pianist. She pretty much hangs around him so much that eventually he stops correcting people that she's not his girlfriend, and even starts referring to her as his girlfriend himself. Eventually a genuine romance blooms and they get married, in one of the few cases where this trope actually works out well for everyone involved.
Yu-Gi-Oh!, Rebecca Hawkins started claiming that Yugi was her "boyfriend" during her second appearance and kept it up through the end of the series. She at least managed to make Yugi blush and Tea jealous if nothing else.
Ranma ½: Tatewaki Kuno, poor deluded fool, is this for any woman he has the slightest interest in. Including (and especially) female!Ranma.
- It apparently runs in the family; his sister Kodachi acts this way toward male!Ranma.

Comics

Peanuts: Sally is like this towards Linus.

"I am not your sweet Babboo!"

Film

Stuntman Mike from Death Proof seems to have this for his victims, but he's a serial killer, and his feelings weren't Played for Laughs.
In Singin' in the Rain, the in-story main couple are rumored to be together -- and Lina goes along with this, because she read it in the tabloids. A few scenes are devoted to Don trying to convince her it isn't true.
The romantic comedy When in Rome runs on this trope with several suitors enthusiastically chasing the protagonist around.
The French film À la folie pas du tout (in English, He Loves Me... He Loves Me Not) features Audrey Tautou as an erotomanic who displays this behavior towards a happily married doctor who is barely aware of her existence. She takes his rejection about as well as you might expect.
Eddie Brock has this opinion of his "relationship" with Gwen Stacy in Spider Man 3. Gwen comments that all they've done is have coffee together.

Live Action TV

Wizards of Waverly Place had Harper dabble in this trope for a few seasons with Justin before moving on to Zeke. She would routinely talk about her (imagined) relationship with Justin and claim that any other girl Justin dated was only a temporary fascination and that he would eventually find his way back to her.
C.C. Babcock on The Nanny sees herself as the only woman in Maxwell Sheffield's life, rather than Fran Fine, even though Maxwell sees her as nothing more than his business partner.
Played for Drama on Dexter, when a murder victim's "girlfriend" turns out to be a stalker who killed him in a rage because he didn't return her feelings.