The phrase "about to finish a" is correct and usable in written English.
It can be used when indicating that someone is on the verge of completing a task or activity.
Example: "I am about to finish a report that is due tomorrow."
Alternatives: "nearly done with a" or "on the verge of completing a".
I am about to finish a novel, so I'm necessarily immersed in the text.
Belfry, the finale of Roche's Wexford Trilogy, is about to finish a short solo run in London.
After a recruiting drive on Somali radio and in newspapers, he had enlisted five hundred young men, who were about to finish a four-month training course.
Shanghai is about to finish a 121-storey American-designed skyscraper that will be the world's second-tallest building (after Dubai's Burj Khalifa).
Some space scientists are about to finish a wearisome six-month stint checking for signs of life on the fiery surface of Mars.
Now Mr. Stone and Mr. Parker are about to finish a video game version of "South Park," and they recently announced that they were forming a production company called Important Studios, valued at $300 million.
The syconium development was relatively shorter during this period and took about 4 weeks to finish a cycle.
It's not about trying to finish a story but instead about illustrating tension, conflicting visions, and complexity.
His next novel, which he's about to finish, is a football-free "teenage romance in which everyone gets blown up", but Peet is sure he'll come back to the beautiful game soon enough.
Just when you think you are watching something funny (such as Simon Pegg in full assassin mode, about to finish off a victim when his mobile phone annoyingly rings) you are confronted with something desperately unfunny (a gruesome killing with slow-motion shots of blood spewing from gunshot wounds).
On the first shift of overtime, the Rangers' Mika Zibanejad was about to finish off a record-breaking game when his shot hit the post.
