Link to the code that reproduces this issue

https://codesandbox.io/p/devbox/nextjs-missing-prefetch-header-5ll75f?file=%2Fapp%2Flayout.tsx%3A38%2C17

To Reproduce

1. Build the application for production
   
2. Run production server
   
3. Inspect the terminal logs when the server starts
   

You will notice that as soon as you load the / page, the middleware logs the pages the current page and also the pages being prefetched, and that later should not happen.

Current vs. Expected behavior

The current documentation suggests that if you don't want the middleware to run for pages that are being prefetched, you can target the next-router-prefetch and purpose headers:

export const config = {
  matcher: [
    {
      source: '/((?!api|_next/static|_next/image|favicon.ico).*)',
      missing: [
        { type: 'header', key: 'next-router-prefetch' },
        { type: 'header', key: 'purpose', value: 'prefetch' },
      ],
    },
  ],
};

Unfortunately that does not seem to work in the latest version of Next.js - those headers are never present, therefore "missing" - so the middleware is running for pages that are being prefetched, which causes issues if you are handling redirects/rewrites, etc...

In my example app, I've a couple Link components in the root layout with a prefetch prop. Those links are being prefetched, but they are also running in the middleware (see the logs) and no prefetch headers are added to those prefetched pages.

I would expect those headers to be available in the middleware for pages that are being prefetched or at least another way for the middleware to know when a page is being prefetched or not.

Provide environment information

Operating System:
  Platform: linux
  Arch: x64
  Version: #1 SMP PREEMPT_DYNAMIC Sun Aug  6 20:05:33 UTC 2023
Binaries:
  Node: 20.11.1
  npm: 10.2.4
  Yarn: 1.22.19
  pnpm: 8.15.4
Relevant Packages:
  next: 14.1.4
  eslint-config-next: 14.1.4
  react: 18.2.0
  react-dom: 18.2.0
  typescript: 5.4.3
Next.js Config:
  output: N/A

Which area(s) are affected? (Select all that apply)

App Router, Middleware / Edge (API routes, runtime)

Which stage(s) are affected? (Select all that apply)

next build (local), next start (local), Vercel (Deployed)

Additional context

I also tested with version 13.5.6 and the issue remains.

I also remove the missing property and added logs to those headers, but they always return as null no matter what.