The phrase "a list of approximately" is correct and usable in written English.
It can be used when you want to indicate that the list contains items that are not exact in number but are close to a certain figure.
Example: "Here is a list of approximately ten ways to improve your writing skills."
Alternatives: "a list of about" or "a list of roughly".
MPs were told that intelligence services had drawn up a list of approximately 20 Islamic fundamentalists who would be detained when the new legislation came into force.
The compounds for the study were chosen from a list of approximately 300 pharmaceutically important compounds, for which multiple crystal forms had not been previously reported.
The committee started with a list of approximately 100 different architecture firms "of the caliber that we associate with MIT," Bacow said.
Both are served as three-course meals accompanied by a choice of teas, which you choose from a list of approximately a dozen varieties.
Using voluntary inventories and government and industry reports, Stringfellow compiled a list of approximately 200 fracking chemicals used in California and 90 chemicals used nationally.
After cutting this list down to eliminate straight-to-DVD or made-for-TV movies, as well as some small foreign films, we get a list of approximately 745 movies.
This led to a list of around 2000 keywords, of which approximately 500 were present in both libraries, of which ten were randomly chosen.
You can find a list of the approximately 200 certified headache doctors on the Migraine Research Foundation's Web site.
Test Your Vocab, a site that collects data for an American-Brazilian research project on vocabulary, age, and education, quizzes each user on forty basic words, then uses the results to compile a test list of approximately a hundred and twenty words that represent the user's vocabulary level.
Google was requested to turn over two items: (1) the results of search queries/requests it received during a one-week period, and (2) a random list of approximately one million URLs searched.
Walmart has identified a list of "priority chemicals" and a shorter list of approximately 10 "high-priority chemicals" that it says it will reduce, restrict, or eliminate in its house brands, and it encourages its suppliers to do the same.
