'keen on writing' is a perfectly correct and usable phrase in written English. It's typically used informally to express enthusiasm for writing. For example, you could say: "My niece is so keen on writing that she often stays up all night to complete her stories."
I'm expecting to hear by every mail from him but he's not very keen on writing letters.
I suspect that she wasn't that keen on writing about writing, or in reading about it.
Though George was based on Larry David, David was keen on writing, and did not have the desire to portray the character himself.
In fact, she wasn't madly keen on his writing.
(Three-day exams, that's how!) Since when are Americans so keen on creative writing that we have to require examples of it for admission to hundreds of schools?
He had to be persuaded to take up the 200m and 400m, and was soon running astonishing times, but "wasn't too keen on training", he writes, and became lazy.
Blunt tells him he should do a PhD, but no one seems terribly keen on his plan to write on the then wildly unfashionable Lawrence Alma-Tadema, so he joins Christie's instead.
Loren King of the Boston Globe isn't keen on "The Oogieloves" either, writing that "it's like paying to watch a dumbed-down mash-up of the least creative parts of 'Teletubbies,' 'Barney & Friends,' and 'Pee-wee's Playhouse.'" King adds that the film's planned interactive moments, during which kids are encouraged to stand up, dance and yell, "seemed more obligatory — you will have fun!
"The late Mr Judd it seems wasn't keen on the minimalist tag," writes Ian Copestake, who has quickly cottoned onto the fact that I don't know anything about art (though I know what I like, and I like what I see, and what I like and see is ART).
He was continuously keen on science popularization and wrote several books and articles for public, such as Secret of Life, Gene and Heredity, Mendel and His Science Career, A Biography for Biologists in Modern China and so on, in which he laid stress on history of science and technology.
"In the Yorkshire philosophy of sport it is impossible to be too keen on winning a competitive engagement," wrote Jim Kilburn, who spent 40 years as the correspondent of the Yorkshire Post, and whose words were, according to Geoffrey Boycott, "read like scripture throughout the county".
I love the desktop app, it’s always running on my Mac. Ludwig is the best English buddy, it answers my 100 queries per day and stays cool.
Cristina Valenza
Retail Lead Linguist @ Apple Inc.