on the verge of
Close to, on the brink of, as in I was on the verge of calling the doctor when he suddenly got better, or Sara was on the verge of tears when she heard the news. This term uses verge in the sense of “the brink or border of something.” [Mid-1800s]
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.