If Reid doesn't do it the record probably will not be broken in our lifetimes with how the modern NFL operates.
For context to break Shula's record would require 35 years of averaging ten wins a year.
The next line of active coaches are Tomlin, John Harbaugh, and Payton and none of them are at 200 yet.
Tomlin is in his early 50s and it doesn't sound like he wants to coach for another 5 years let alone the necessary 15-20.
Harbaugh and Payton are in their 60s already so unless they coach into their late 70s they probably don't have a real shot at it from a time perspective.
McVay could possible do it if he wants to coach another 20-25 years, but he has indicated he has other aspirations than coaching.
The only current wild card is Belichick, but his days as an NFL coach appear to be over.