Currently, guidance says Police forces should only issue penalties when motorists are 10% over a speed limit plus 2mph - for example, 35mph in a 30mph zone.
But chief constable Anthony Bangham, the National Police Chiefs' Council lead on road policing, is said to have called for an end to the 10% "buffer".
Mr Bangham said speeding awareness courses were being used too widely instead of penalty points and fines.
The West Mercia chief made the comments in a speech at the Police Federation Roads Policing Conference on Tuesday, according to the Daily Mail.
He was quoted as saying: "Let's change the message - we are proud to be law enforcers.
"I do not want the public to be surprised, I want them to be embarrassed when they get caught... They need to understand the law is set at the limit for a reason.
"They should not come whinging to us about getting caught. If booked at 35 or 34 or 33 (in a 30mph zone) that cannot be unfair because they are breaking the law."
Tory MP Sir Greg Knight warned against an "overly aggressive policy against drivers".