Although not hearing impaired, I watch television with captions enabled. I like to see how words are spelled and how the running text differs from what is actually said by the actors and presenters. When I began to notice a frequency of the spelling gonna for “going to,” I decided to do a little research.
I discovered that gonna has an entry in the OED:

gonna: colloquial (especially U.S.) or vulgar pronunciation of “going to.”

Not only gonna, but wanna, gotta, and shoulda also have entries in OED, although they do not appear in Merriam-Webster.

Gonna, gotta and wanna are not contractions.

Contractions are shortenings like aren’t and can’t. The missing letters have been replaced by an apostrophe, and the original words are discernible in the contraction.
Contractions are acceptable in all but the most formal writing. Here are a few standard contractions:

aren’t = are not
can’t = cannot
couldn’t =could not
didn’t = did not
doesn’t = does not
don’t = do not
hadn’t = had not
hasn’t = has not
haven’t = have not
he’d = he had, he would
he’ll = he will, he shall
he’s = he is
I’d = I had, I would
I’ll = I will, I shall
I’ve = I have
isn’t = is not
it’s = it is
let’s = let us


The spellings gonna, gotta, and wanna, on the other hand, do not preserve the shape of the words they represent. They are not contractions, but reductions.

A linguistic reduction is the result of relaxed pronunciation. All speakers of all languages slur sounds and words together. Doing so is a normal part of spoken language. The more informal the situation, the more slurring goes on.

Speakers who are sensitive to the needs of others will speak more carefully in some situations than in others. For example, teenagers who barely move their lips when speaking to one another may be expected to enunciate in the classroom.

Courteous native speakers will take the trouble to pronounce words carefully when speaking to non-native speakers. Any English speaker who has received a formal education of ten years or more may be expected to speak clearly when being interviewed on television.
Reductions are not unknown in print. Novelists have long spelled out whatcha and coulda in dialogue in order to convey a character’s attributes. Until recently, however, such spellings were not commonly seen outside of fiction.

Gonna and gotta are not unexpected in song lyrics and on social media like Facebook, but now they are creeping into news coverage. Here are some examples from transcripts and quotations that have appeared on news sites:

“He’s gonna get to the bottom of what happened at the Fort Hood shooting.”
“I have no doubt she’s gonna run,” says Black.
“We’re gonna try to construct a bipartisan bill.”

Reductions heard in speech are not particularly jarring, but when they appear in print, they scream “Ignorant!” Unless a journalist desires to present a senator in a negative light, “going to” is a better choice than gonna, even in a direct quotation.
Professional writers especially might be expected to avoid nonstandard usage and spelling, but the evidence on Amazon is that for many authors, gonna, gotta, wanna, and even whatcha and coulda are acceptable written English. Here’s a sampling of book titles:

Dude, You’re Gonna Be a Dad!
10 Things You Gotta Know About Choosing a College
I Wanna Iguana (This one is the title of a children’s book.)
Whatcha Gonna Do with that Duck?
Coulda Been a Cowboy

Time will be the judge. An Ngram search shows that the use of gonna in printed books has risen dramatically since the 1960s, and gotta and wanna are making a little progress.
It’s possible that these words will become acceptable in standard English one day. Meanwhile, their use does not reflect well on writers who wish to be taken seriously.