The phrase "approaching the completion" is correct and usable in written English.
It can be used to indicate that something is nearing its end or final stages.
Example: "The project is approaching the completion, and we expect to finalize it by the end of the week."
Alternatives: "nearing completion" or "close to finishing".
He wrote his moving book When Breath Becomes Air as he approached the completion of his training as a neurosurgeon, but after he had developed metastatic lung cancer.
As he approached the completion of his second year as the Conservatives' director of communications, Coulson could hardly have been in a stronger position.
"As we approach the completion of our upfront sales process, we are very pleased with the strength of this year's marketplace," said a spokesman for CBS, Dana McClintock.
Howard's departure from the Mets after more than 20 years comes as the Garden approaches the completion of a nearly $1 billion renovation.
Dr. Fratkin has created ResolutionCare to bring capable and compassionate care to everyone, everywhere as they approach the completion of life.
As we approached the completion of Zaide's missing third act, we questioned again whether forgiveness was believable after the years of violence, slavery, and sexual exploitation described in the opera.
As you approach the completion of your Ph.D. program, you will need to following the appropriate process for graduation.
Armitage was approached following the completion of the second series of Robin Hood, for which he portrayed the regular part of Sir Guy of Gisbourne.
The Government, though so slow in building new frigates that none took part in the war, had in the latter part of 1813 three new sloops approaching completion, the Peacock, the Frolic, and the Wasp, names given in honor of Lawrence's and Jones's splendid victories.
The approaching completion of the Malaysian refinery, with the capacity to meet a fifth of the world's demand, has contributed to the plunge.
