on the point of
Also, at the point of. On the verge of, close to, as in I was on the point of leaving when the phone rang. The first term dates from the late 1200s, the second from the first half of the 1500s.
The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 2003, 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.