The phrase "keenly seeking" is correct and usable in written English.
It can be used to express a strong desire or eagerness to find or obtain something.
Example: "She is keenly seeking new opportunities to advance her career."
Alternatives: "eagerly searching" or "intently looking for".
The methane reserves are converted to liquefied natural-gas, which is keenly sought after in the Asia- Pacific region.
Fluency in English and internationally recognised qualifications are keenly sought as China opens up to the world.
Eager to stimulate its feeble economy, Jordan had keenly sought the agreement for more than a year.
All three keenly seek to raise their influence among other things by trying to bolster the electoral chances of those Iraqis with whom they have most in common.
The lovely irony is that he enjoys the renown his dad so keenly sought for his dusty library of neglected Afrocentrists.
"I wouldn't say there's anxiety," Wright-Phillips says, when it is put to him that the presence of Lennon and Theo Walcott make the right midfield squad positions the most keenly sought after of all.
I lived in Liberia for a year as an adolescent boy, in the early nineteen-seventies, and keenly sought out opportunities to get into the country's remote interior in the hopes of seeing wildlife.
Industrious, amiable, and shrewd, surrounded by his modest household, and keenly sought after as an artist, he pursued a successful career into old age and amassed a comfortable fortune.
Niche producers on this rugged 285-mile-long island with a temperate climate not unlike Cornwall are wooed by restaurants; their ciders and fresh veg keenly sought out at the farmers' markets.
News that the Sun's political editor, George Pascoe-Watson, has tutored the shadow cabinet on how to deal with the media may cause excitement in political circles since the paper's support is keenly sought by the Tories.
